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Full text of "Jesuits on the moon : seeking God in all things-- even mathematics!"

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THE 



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Jesuits on the Moon 

Seeking God in All Things . . . Even Mathematics! 



Dennis C. Smolarski, S.J. 



BX3701 S88x 

Studies in the spir.tuality of Jesuits 

Issue: v.37:no.1(2005:spr,ng) 

Arrival Date: 04/01/2005 

O'Neill Current Periodicals 



a • SPRING 200£ 



THE SEMINAR ON JESUIT SPIRITUALITY 

The Seminar is composed of a number of Jesuits appointed from their provinces in the 
United States. 

It concerns itself with topics pertaining to the spiritual doctrine and practice of 
Jesuits, especially United States Jesuits, and communicates the results to the members of 
the provinces through its publication, STUDIES IN THE SPIRITUALITY OF JESUITS. This is 
done in the spirit of Vatican Li's recommendation that religious institutes recapture the 
original inspiration of their founders and adapt it to the circumstances of modern times. 
The Seminar welcomes reactions or comments in regard to the material that it publishes. 

The Seminar focuses its direct attention on the life and work of the Jesuits of 
the United States. The issues treated may be common also to Jesuits of other regions, to 
other priests, religious, and laity, to both men and women. Hence, the journal, while 
meant especially for American Jesuits, is not exclusively for them. Others who may find 
it helpful are cordially welcome to make use of it. 



CURRENT MEMBERS OF THE SEMINAR 

James W. Bernauer, S.J., teaches philosophy at Boston College, Chestnut Hill, Mass. 
(2004). 

Richard A. Blake, S.J., is chairman of the Seminar and editor of STUDIES; he teaches 
film studies at Boston College, Chestnut Hill, Mass. (2002). 

Kevin Burke, S.J., teaches systematic theology at Weston Jesuit School of Theology, 
Cambridge, Mass. (2003). 

Gregory C. Chisholm, S.J., is administrator of Holy Name of Jesus Parish, in South 
Los Angeles, Cal. (2003). 

T. Frank Kennedy, S.J., teaches music and is director of the Jesuit Institute at Bos- 
ton College, Chestnut Hill, Mass. (2004). 

Thomas P. Rausch, S.J., teaches theology at Loyola Marymount University, Los 
Angeles, Cal. (2002). 

William E. Reiser, S.J., teaches theology at the College of the Holy Cross, Worces- 
ter, Mass. (2004). 

Thomas L Schubeck, S.J., teaches social ethics at John Carroll University, Univer- 
sity Heights, Ohio (2004). 

Dennis C. Smolarski, S.J., teaches mathematics and computer science at Santa Clara 
University, Santa Clara, Cal. (2003). 

The opinions expressed in STUDIES are those of the individual authors thereof. 
Parentheses designate year of entry as a Seminar member. 

Copyright © 2004 and published by the Seminar on Jesuit Spirituality 



Publication Office 

Studies in the Spirituality of Jesuits 
3601 Lindell Blvd., St. Louis, MO 63108 
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(E-mail ijs@slu.edu 



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Jesuits on the Moon 

Seeking God in All Things . . 
even Mathematics! 



Dennis C. Smolarski, S.J. 



STUDIES IN THE SPIRITUALITY OF JESUITS 

37/1 • SPRING 2005 



The first word . . . 



For such a young man, St. John Berchmans demonstrated extraordinary 
insight when he reputedly said, "My penance is to live the common life." 
This is the Catholic Encyclopedia's bland translation of the more pointed 
version I recall from an earlier life: "Vita communis, crucifixio maxima." In 
other words, the boy-saint from Belgium seemed to imply that the breth- 
ren can be a real pain in the nether-lands at times. 

Here's one source of the problem. Jesuit communities seem to have 
been targeted by an unending supply of appliance terrorists, who must 
have a secret training base somewhere in the Carpathian Mountains near 
the legendary castle of Count Dracula. Natural talent and serendipity 
could not explain their astounding success through the years, if not the 
centuries. Some day I would like to team up with a Scripture scholar who 
understands the vagaries of the oral tradition and a postulator or "devil's 
advocate" who can help investigate these stories and track down the frag- 
ments of truth that lurk somewhere in the legends of community life. 
Perhaps we could even begin a new television series: CSI: Haustus Room. 

Every province has its own anthology of epic incompetence in the 
aftermath of the industrial revolution. Here are a few that I've gathered 
from my travels around the Assistancy, some of which may indeed contain 
more truth than we'd like to imagine. Some involve only limited impact on 
the community, like the man who was delighted to find a washing machine 
in the kitchen of his new apartment, and then shredded his clothes into a 
mass of soggy lint in the dishwasher. Sometimes the effect strikes the 
group as a whole. For example, one newcomer to the domestic arts once 
heard the household hint that placing a sneaker in the dryer would help 
"fluff up" his clothes. Lacking a sneaker, he used a brick doorstop, thereby 
reducing the drum of the machine to an abstract expressionist sculpture. 
Sadly, no photographer was present to catch the expression of disbelief on 
the face of the Maytag repairman, but the others in the residence went 
several days without a washer. 

Haustus rooms or pantries have always been soft targets for surrepti- 
tious attacks. Ministers should have a Website to exchange and collect 
stories, with or without Celtic embellishment. One poor minister bought a 
"big mouth" toaster to enable his charges to brown a morning bagel with- 
out having to risk electrocution by using a fork to dislodge it from a stan- 
dard-size model. Big mistake. Obviously, according to one man's percep- 
tion, the device was intended for grilled-cheese sandwiches, which of 
course melt and flow onto the coils, causing both a rancid fire and a short 



122 



circuit. I have heard a story about the man who found a new table-top 
television set on the counter next to the coffee maker. All set to enjoy a 
newscast with his morning caffeine fix, he punched in the numbers of his 
favorite station. A light went on, the gadget made a whirring noise and the 
numbers on the channel selector decreased, one per second until the light 
went out and the whirring stopped. He tried again. Same result. Of course, 
he complained that the minister had bought a cheap TV set that didn't 
work worth a damn. So much for the new microwave oven. And speaking 
of microwaves, how many communities have had to clean up the mess 
when someone decided to save time by zapping an egg rather than boiling it? 

Coffee makers seem a particularly vulnerable target of opportunity. 
One despairing villa superior went shopping for yet one more replacement 
with the determination to find an "Ours-proof ' machine. It would have no 
moving parts, no detachable elements, an automatic turn-off feature, a 
metal basket and pot, and a large sign in flashing letters warning Sergeant 
Starbuck, S.J., that the receptacle is intended to take only water for fresh 
brewing, not yesterday's dregs for recycling. Even if such a device could be 
found, it would provide only temporary respite. Terrorists traditionally 
change their tactics in response to new security procedures. Martha Stew- 
art, come to our assistance; Emeril, make haste to help us. 

The exploits of Ours in the automotive age outpace the imagina- 
tions of Jules Verne and George Lucas combined. Every province seems to 
have a car that was discovered parked sideways in a garage. One of our 
veteran drivers, hovering on the edge of being grounded, managed to 
remove two rear-vision mirrors on two cars on two successive days. Know- 
ing that a preemptive strike might delay the minister's (the rector's, and 
the provincial's) anticipated move, he invaded the rector's office expressing 
outrage at the stupidity of superiors for installing garage doors that were 
too narrow for the cars. Another driver parked a house car on a hill in 
front of the residence, and watched as it rolled down the slope, through a 
hedge, across a lawn, and into another building. He explained that the gear 
shift was stuck and he could not get it into "park." When asked about the 
parking brake, he expressed amazement, since he had never heard of such 
a strange device. This could only be matched by the Jesuit who was frus- 
trated at not being able to follow a breaking news story on his radio be- 
cause he had it set to listen to classical music and was not aware that he 
could change the station. 

Community computers and photocopiers have opened up entirely 
new horizons of possibility that would clearly strain the space constraints 
of this column. To borrow the words of an earlier spiritual writer, "If these 
things were to be described individually, I do not think the whole world 
would contain the books that would be written" (John 21:25). 

Some of these stories may actually be true, at least a little bit. The 
oral tradition within the Society demands study in itself. We had a won- 



IV 



derful story in the Maryland and New York provinces about an Irish-born 
brother at Port Kent, the villa for philosophers on Lake Champlain near 
the Canadian border of New York State. Zealous to protect the reputa- 
tions of the pious scholastics, he dismissed a deliveryman's comment about 
the amount of beer he had just unloaded by telling him it was for "a thou- 
sand men." Imagine my amazement, sitting at evening seminar in a Mid- 
western community several years ago and hearing the same story, word-for- 
word, about a German-born brother at Waupaca, the villa for Wisconsin 
scholastics. No one should be surprised to hear the same story about an 
old Italian-born brother at Applegate, the California villa, but there the 
delivery would probably have been zinfandel or mineral water. The oral 
tradition has a tendency to take on a life of its own. 

The phenomenon raises two intriguing questions. First, why does 
this caste of dedicated Jesuit appliance terrorists renew itself year after year 
in such a stunning variety of manifestations and with a seemingly inex- 
haustible capacity to redirect its energies to ever-newer forms of technol- 
ogy, and second, why do we continue to compile their acta and lovingly 
embroider them with fanciful glosses on the Urtext? 

The first question seems fairly straightforward. We aren't competent 
in dealing with worldly matters, because we don't have to be. Clearly, most 
of us have never negotiated a mortgage, bought insurance, or filled out a 
tax return, the kinds of routine tasks that generally define responsible 
adulthood in our contemporary world. This distance from mundane experi- 
ences carries over into the trivia of human life. If we had to pay for trash- 
ing a washing machine or coffee maker out of our own pockets, or call a 
repairman, or shop for a replacement, chances are we would be more 
willing to read the instruction booklets and pay attention to what we were 
doing. In community living, somebody else takes care of such things. 

"Irresponsibility" in both senses of the word is an inevitable result 
of living in the "total" institution. The concept comes from an Erving Goff- 
man's Asylums, a classic fifty-year-old study on social psychology that still 
provides fascinating insights for those of us trying to understand "the 
course." Goffman links the common elements in various forms of tightly 
controlled social structures, like military boot camps, prisons, long-term 
medical facilities, and — believe it or not — convents, monasteries, and semi- 
naries. For the organization to work, newcomers have to surrender individ- 
uality and become totally dependent on "the system," with its clearly 
established hierarchies and well-defined rituals. In its most extreme forms, 
in the old novitiates, for example, one novice was a shoe beadle, who alone 
could take shoes for resoling, and another a sock beadle, who kept the 
common-stock sock box filled. From an institutional standpoint, it makes 
perfect sense. It is clearly better to have one man learn how to wash socks 
than have many learn how to operate the machinery. From a personal 
standpoint, it's disastrous. Even outside the large houses of formation, a 



Jesuit was expected to "put a note in the minister's box" rather than 
change a light bulb, which he couldn't do anyway, since for years light 
bulbs were kept in a locked closet. 

Why? The institution is slow to change such insane practices, ac- 
cording to Goffman, because a loosening of the rules could jeopardize the 
social structure by undercutting the control and thus the power of the 
authorities: the minister, the brother, and now the lay custodian who has 
to maintain his indispensability to keep his job. Sadly, too, honesty de- 
mands the admission that a loosening of long-established restraints could 
predictably lead to abuses of new-found freedoms and brick-in-the-dryer 
incidents. In some dark moments, the price we pay for "deinstitutionaliza- 
tion" makes the old days of the "long black line" seem rather attractive. 
Goffman 's study provides the consoling realization that the effects of insti- 
tutional living are not unique to Jesuits, but that they are risks found in 
many controlled social structures. 

(Younger Jesuits, who have always lived in smaller communities 
where personal responsibility is presumed, don't know what this is all 
about. Good. That's a sign of real progress. I invite them to read on in the 
hope that this reflection might help them understand why some of us 
older types are so weird.) 

Goffman is helpful in addressing the second question: Why do our 
appliance terrorists assume legendary status in our oral tradition when in 
fact they should be a source of embarrassment? In his analysis, those who 
obstruct the system by frustrating its goals and humiliating its hierarchy 
are perceived as heroes for asserting the role of the individual over the 
organization. The few give voice and gesture to what is felt by the many. 
Institutions frequently provide this outlet as one of its condoned rituals. 
Christmas shows, for example, sanction entertainment that includes unflat- 
tering imitations of guards, nurses, boarding-school teachers, and seminary 
professors. In the military or on shipboard, this outlet takes the form of 
creative griping about officers. The best impressionists and most incisive 
critics gain prestige among their peers for their daring defiance of the 
system. They say what others think. 

Jesuits who wreck coffee makers and computers, despite the inconve- 
nience they cause others, fit into this pattern of admired defiance. Ma- 
chines are a form of institution; they rule our lives, degrade us, and make 
us conform to their own priorities, not through their own conscious design, 
but through the imperious regulations that surround them, like "you have 
performed an illegal function and will be shut down." In a perverse way, 
we admire the appliance terrorists for swimming against the tide of history, 
even though they drive us crazy at times. By telling and retelling their 
stories, we have it both ways. We enshrine their acts of defiance and make 
them our own. At the same time, we distance ourselves from the hapless 
and malicious, and situate ourselves in a somewhat superior position. 



VI 



Boasting of an inability to add toner to the copier somehow places us 
above such trivial details, and at the same time we assure ourselves that we 
are more attuned to modernity than the colleague who tried and did sev- 
eral hundred dollars' worth of damage to the defenseless machine. 

It seems hard to believe that this ubiquitous Marching Band of 
Benevolent Luddites has in fact fallen out of step with the oldest traditions 
of the Society of Jesus. During the age of exploration, Jesuits were the 
sixteenth-century equivalent of Silicone Valley techies. They may even 
have worn plastic pocket protectors inside their soutanes. Their ability to 
predict eclipses and fashion a more accurate calendar matches the achieve- 
ment of today's Mars rover. Just like us, early Jesuit scientists and mathe- 
maticians probably had to live with people who could break a doorknob by 
looking at it. These ham-fisted brethren couldn't tell an alembic from an 
astrolabe, but that didn't stop them from denouncing all these new-fangled 
gadgets as witchcraft. Despite the fulminations of their less perceptive 
brethren, Jesuit mathematicians moved ahead in their research and their 
effort to spread the word that science and technology had a place in the 
universities, alongside metaphysics and logic. 

In this current issue of STUDIES, Dennis Smolarski has assembled a 
fascinating account of early Jesuits in their more successful encounters 
with modernity. These men used their mathematics and science as apos- 
tolic instruments to enhance the Good News for the intellectual elites of 
their own world and build bridges to the cultures of Asia. Much of this is a 
familiar story that needs to be retold. Finally, Dennis offers a reflection for 
each of us today on the role of the sciences in our ongoing search for God 
and God's ongoing search for us. 



Richard A. Blake, SJ. 
Editor 



Vll 



CONTENTS 



I. Introduction 1 

Seeking God in All Things 2 

Going In by Our Neighbor's Door 3 

Overview 5 

II. Three Vignettes 5 

Christopher Clavius 6 

Matteo Ricci 9 

Francois d'Aguilon 12 

III. Mathematics, the Early Society of Jesus, and the 

Ratio studiorum 12 

Academic Climate in Italy 14 

The Nascent Scientific Revolution 16 

The Influence of Clavius on the Ratio studiorum 16 

The Evolving Ratio studiorum 20 

IV. The Definitive 1599 Ratio studiorum and the Revised 

Ratio of 1832 22 

V. Reflections 24 

Seeking and Finding God 25 

The "Desires" and Insights of Clavius 29 

Contemporary Jesuit Scientific and Technical Ministries 30 
Educational Challenges: Jesuit Formation 

and Academic Institutions 31 

VI. Concluding Thoughts 35 

Appendix 1: Jesuit Craters on the Moon 37 

Appendix 2: "De mathematicis" 39 

Appendix 3: Excerpts from Rules for Mathematics 41 

Documents and Translations 42 



IX 




mm 

- 

■ 






33 






The Moon with Craters Named after Jesuits Indicated 
(See Appendix I) 



Dennis C. Smolarski, S.J., graduated from Santa Clara 
University as a math major before entering the Cali- 
fornia Province in 1969. After ordination, he earned 
his Ph.D. in computer science at the University of 
Illinois at Urbana. While teaching mathematics and 
computer science at Santa Clara, he has been working 
on a computer model for supernovae for the Depart- 
ment of Education. In addition to his specialized re- 
search, he has been involved in liturgy and the Byzan- 
tine Catholic parishes around San Francisco. He is the 
author of the widely known How Not to Say Mass 
(Paulist) and Q and A: Seasons, Sacraments, and Sacra- 
mentals (Liturgical Press). 



Jesuits on the Moon 

Seeking God in All Things . . . Even Mathematics! 



In sixteenth-century Europe several Jesuits pioneered formal 
studies in mathematics and science and used their research 
to begin a dialogue with Asian cultures. Their attempt to 
include mathematics in the university curriculum in Italy 
was nothing short of revolutionary. The need continues 
today, as the contemporary world presumes a greater level 
of technical competence than ever before. In a wider context, 
mathematics provides a means to contemplate the wonders 
of Gods universe. 



I. Introduction 

Atypical reaction to the title of this issue of STUDIES might well 
be, "Jesuits on the moon? Surely you jest!" But "jest" I do 
not! Even though no member of the Society of Jesus has 
actually stepped foot on the moon (at least as of Christmas 2004), the 
memory of Jesuit scientists has, nevertheless, become a permanent 
part of the map of the moon because about thirty-five craters have 
been named after our brothers in the Society (see frontispiece and 
Appendix 1). These men studied mathematics, astronomy, and 
physics (among other sciences), although the modern names given 
to distinct academic disciplines often do not do justice to the breadth 
of the scientific interests of these Jesuits. In turn, history has re- 
warded them for their scientific expertise (and honored the Society 
through them) by associating their names with the lunar landscape. 

The Society has an honored tradition of involvement in math- 
ematics and the natural sciences and this essay is a modest attempt 
to help readers recall that tradition, and to raise some questions 
about the future of that tradition. But let me begin by suggesting 
that a number of early Jesuit scientists devoted themselves enthusi- 

1 



2 <0> Dennis C. Smolarski, SJ. 



astically to scientific study prompted by two fundamental spiritual 
principles that are part of our living heritage as Jesuits, namely, 
(1) striving to seek and find God in all things (yes, even in disci- 
plines as abstract as mathematics!) and (2) using whatever means are 
appropriate (even using mathematics and natural sciences) to "go in 
our neighbor's door but come out our own/' Let me begin with a 
brief reflection on these two Ignatian principles to help provide a 
context for the remainder of this essay. 

Seeking God in All Things 

In the Constitutions of the Society of Jesus, St. Ignatius writes that 
Jesuits should "seek God in all things." 1 Later, in ConsCN C 451 vl , 
mathematics is mentioned as one of the topics to be taught in the 
schools of the Society, but reference to mathematics is phrased in 
such a way, "and also mathematics," that one suspects that its 
inclusion may have been considered unusual, given the academic 
climate of sixteenth-century Italy. 2 Yet part of our Jesuit spirituality, 
an incarnational spirituality, is that God can, indeed, be found in "all 
things," whether it be in the Christian community gathered at the 
Eucharist and in the sacramental elements themselves, or in the 
abstractions developed by our God-given intellectual gifts, whether 
those abstractions describe moral laws, theological truths, or mathe- 
matical structures. 

In Mere Christianity, C. S. Lewis wrote, "[God] likes matter. He 
invented it." 3 With a perspective such as this, we should be able to 



The Latin text reads "ut in omnibus queerant Deum." This seems to be the base 
text for the more commonly used expression, "rinding God in all things" (ConsCN C 
288 v3 [p. 124]). See The Constitutions of the Society of Jesus and Their Complementary 
Norms: A Complete English Translation of the Official Latin Texts (St. Louis: The Institute 
of Jesuit Sources, 1996). Hereafter this source will be abbreviated to ConsCN, followed 
by C and the boldface marginal number introducing each section and, when useful, 
the "verse number." 

2 

The Latin text reads "et etiam mathematicee." The presence of the etiam ("also, 
even") argues for the unusual nature of including mathematics (mathematical 
sciences/topics) in a university curriculum. See the discussion on pp. 44 f. by Jeffrey 
Bloechl in his article, "The Jesuit Ratio Studiorum and the Teaching of Mathematics: 
On the Incursion of Modern Rationality into a Classical Pedagogy," Fundamental 
Questions: A Journal of the Liberal Arts 1, no. 1 (Fall 2004): 41-60. 

3 

C. S. Lewis, Mere Christianity (New York: Macmillan, 1960), 65. 



Jesuits on the Moon <& 3 



find God in material creation as well as in the ways human beings 
have devised to depict or describe that creation, such as abstract art 
or applied (and abstract) mathematics. Galileo considered that the 
"book" that is the universe "is written in the language of mathemat- 
ics," 4 and many contemporary mathematicians and scientists would 
agree that mathematics does indeed provide the language for the 
world of science and technology. That they look at and reflect on the 
beauty (and interrelatedness) of God's creation (which includes 
mathematics) is what Ignatius asks of retreatants both in the Princi- 
ple and Foundation and in the Contemplation to Attain Love. 5 There 
is a long tradition of Jesuits being actively engaged in mathematical 
and scientific research as a major means for them to come to a 
deeper understanding of the creation in which we all continue to 
seek and find our God. The better human beings come to under- 
stand and describe creation, the better we may be able to cooperate 
with God in building up the Kingdom on earth for the benefit of 
future generations. Although each Jesuit's description of how he 
actually "finds God" in mathematics may be as unique as each Jesuit, 
many (myself included) see in mathematics a glimpse into the order, 
cohesiveness, and beauty that is of the nature of divine realities. 6 



Going In by Our Neighbor's Door 

In explaining St. Paul's words "I became all things to all so as 
to win some to Christ" (1 Cor. 9:22), Ignatius wrote the following to 
Alonso Salmeron, S.J., and Paschase Broet, S.J., in 1541 as they were 
setting off to Ireland as papal legates: "Whenever we wish to win 
someone over and engage him in the greater service of God our 
Lord, we should use the same strategy for good which the enemy 



Galileo, The Assayer (1623). See Stillman Drake, Discoveries and Opinions of 
Galileo (Garden City: Doubleday Anchor Books, 1957), 237 f. 

See The Spiritual Exercises of St. Ignatius, trans, with commentary by George 
E. Ganss, S.J. (St. Louis: The Institute of Jesuit Sources, 1992). Hereafter this source 
will be abbreviated to SpEx. The quotations here are from SpEx nos. 23 and 234f. (pp. 
32 and 94f.). 

Thomas Aquinas's "Fifth Way" for proving the existence of God is related to 
order found in the universe (Summ. TheoL, pt. 1, quest. 2, art. 3). For another 
contemporary Jesuit's reflections on finding God in science, see "Finding God in 
Creation," in Brother Astronomer: Adventures of a Vatican Scientist, by Guy J. Con- 
solmagno (New York: McGraw-Hill, 2000), pt. 2, pp. 99ff. 



4 <0> Dennis C. Smolarski, S.J. 



employs to draw a good soul to evil. He enters through the other's 
door and comes out his own." 7 Jeronimo Nadal, summarized these 
thoughts of Ignatius in the often repeated Jesuit maxim, "Enter by 
their door so as to come out by our door/' 8 

One of the earliest examples of a Jesuit using mathematics as 

the "other's door" in the hope of 
drawing someone to Christianity, 



What I would like to reflect was Matteo mcci (1552-1610), the 

upon in this essay is the am u ed J""* missi °™ry * China. 

* jm.- j r • 4. t In his dealings with Qu Rukuei, a 

tradition and history of ■ , ° , , r 

., .. , j i Confucian scholar a few years 

mathematical study, research, ., Ll . _,. . /, 

, . ^ n t ' older than he, Ricci was able to 

and use in the Society. ^ , , . . , 

u wean Qu from his interest in al- 

. chemy to mathematics. Ricci's ap- 

proach was to start with mathe- 
matics, however, and only when appropriate speak about religious 
topics. As Ronald Modras notes, 

[Ricci] laid open to Qu the world of Euclidian geometry with its 
axioms and deductions, and, when the opportunity arose, he related 
something about Christianity. Qu proved an adept student. He took 
careful notes and astounded his teacher one day with a series of 
perceptive questions about the Christian faith, all deriving from a 
Confucian scholar's perspective. The exchange proved significant for 
master and disciple alike. Qu eventually became a Christian, and 
Ricci learned the importance of relating Christianity to someone 
steeped in Confucian tradition. 9 



7 

Letters of St. Ignatius of Loyola, trans. William J. Young (Chicago: Loyola 
University Press, 1959), 51 f. Also see the discussion on "Going In by His Door," in 
The Conversational Word of God, by Thomas H. Clancy, S.J. (St. Louis: The Institute of 
Jesuit Sources, 1978), 26-28. 

Q 

In "Jeronimo Nadal's Sixth Exhortation (chap. 4, par. 26), we read: "But in 
these exchanges one should watch carefully for an occasion to give the conversation 
a religious turn. Father Ignatius used to speak of this method as 'entering by their 
door so as to come out by our door.' He was not in favor of launching forth 
immediately on virtues and vices, the life of Christ, and the last things, because in 
this way our hearers never really get interested in what we are saying, but are 
rendered inattentive by our untimely zeal" (English translation in Clancy, 
Conversational Word of God, 54). 

9 

Ronald Modras, Ignatian Humanism (Chicago: Loyola Press, 2004), 105. 



Jesuits on the Moon -0- 5 



Overview 



What I would like to reflect upon in this essay is the tradition 
and history of mathematical study, research, and use in the Society 
and, by extension, the pursuit, by Jesuits, of other forms of scientific 
and technical knowledge. My reflection is influenced by my own 
"seeking God in all things," particularly in mathematics and com- 
puter science, since those are the disciplines I have studied and they 
are what I teach. It goes without saying that the contemporary 
society in which we live is one in which science and technology play 
ever-greater roles. At the same time, I, for one, notice an ever-in- 
creasing gap between those comfortable with modern technology 
(aside from surfing the "Net/ 7 and using e-mail or word-processing 
programs) and those (Jesuits included) who seem to feel that the 
farther they stay from mathematics and other technical fields, the 
better! One hope of mine is that in the future, more Jesuits may be 
able to help close the technological "gap" evident in our society, 
since Jesuits have had a long and distinguished history of scholar- 
ship in mathematics and scientific disciplines. 

I will first offer brief vignettes of three Jesuits who were 
actively engaged in mathematics and science to remind the reader of 
early Jesuit scientific history, particularly in light of the two princi- 
ples just mentioned. Then I will turn my attention to the place of 
mathematics in the early Society, by looking at the curriculum of 
Jesuit schools as incarnated in the Ratio studiorum, the first guidelines 
for a "core curriculum" for Jesuit schools as well as a handbook for 
faculty and administration. Finally, I will offer some personal reflec- 
tions and concluding thoughts on mathematics and technical disci- 
plines today. 

II. Three Vignettes 

To help the reader recall part of our Jesuit tradition regarding 
mathematics and related sciences, let me present brief vi- 
gnettes of three Jesuit scientists: Christopher Clavius, whose 
enthusiasm in seeing mathematics in every human discipline is 
reminiscent of Ignatius's maxim to seek God in all things; Matteo 
Ricci, who is a prime example of someone who entered through his 
neighbor's door to attempt to bring the neighbor out our own; and 
Francois d'Aguilon, who brought to fruition the dream of Clavius to 



6 ^ Dennis C. Smolarski, SJ. 



have a Jesuit "academy" of mathematics that would attempt to carry 
on the newly established scientific tradition of the Society. 10 

Christopher Clavius 

Christopher Clavius was born in Bamberg (Germany) in 1538. 
In 1555 he traveled to Rome to join the Society and in 1564 was 
ordained a priest while finishing theology at the Roman College. He 
began teaching mathematical subjects at the Roman College around 
1564 and continued for about forty-five years, until his death in 1612 
(except for two years around 1596 when he was in Naples and 
Spain). 11 Documents from the Roman College indicate that Clavius 
was the sole teacher of mathematics for at least twenty-two years 
between 1564 and 1595. 12 

One of Clavius's major accomplishments was his influence on 
the revision of the calendar. In 325 the Council of Nicea had set the 
date of Easter as the first Sunday after the first full moon after the 
vernal equinox, which marks the start of spring. The full moon 
corresponds to the middle day (fourteenth day) of a Hebrew (lunar) 
month of twenty-nine days (which always begins with a new moon). 
Thus, the seemingly odd rule for computing Easter is an attempt to 
situate Easter as the first Sunday after the beginning of Passover, 
which should always occur on the fourteenth day of Nisan (Exod. 
12:6), the first spring month of the Hebrew calendar. 

Since the actual length of an astronomical earth year is slightly 
less than 365.25 days, the Julian calendar in use in the Roman 
empire, with its unvarying rule of inserting a leap day every four 
years, overcompensated in trying to adjust calendar dates to match 
astronomical dates (in particular, in trying to synchronize the first 



Sections 2-4 are based on what is presented in "The Jesuit Ratio Studiorum, 

Christopher Clavius, and the Study of Mathematical Sciences in University/' by 

Dennis C. Smolarski, Science in Context 15, no. 3 (2002): 447-57. Also see Dennis C. 

Smolarski, "Teaching Mathematics in the Seventeenth and Twenty-First Centuries," 

Mathematics Magazine 75, no. 4 (Oct. 2002): 256-62. 

11 
An in-depth look at the life of Christopher Clavius, S.J., may be found in 

Between Copernicus and Galileo: Christoph Clavius and the Collapse of Ptolemaic Cosmology, 

by James M. Lattis (Chicago: The University of Chicago Press, 1994). On p. 23 Lattis 

suggests that Clavius may have left Rome because of health problems. 

12 

William A. Wallace, Galileo and His Sources: The Heritage of the Collegio 
Romano in Galileo's Science (Princeton: Princeton University Press, 1984), 7. 



Jesuits on the Moon -0- 7 




Christopher Gavins, S.J. (1538 - 1612) 

day of spring always as March 21). By the beginning of the sixteenth 
century, the calendar date was ten days later than the astronomical 
date, that is, the beginning of spring was celebrated on what we 
would now consider to be March 31 rather than March 21. 13 Astrono- 
mers who determined the beginning of spring by the height of the 
sun in the sky (and thus the length of shadows) raised concerns 
that, without some sort of calendar correction, the official beginning 
of spring (on the calendar) might eventually move so that Easter 
(around the middle of the first month of spring) would be celebrated 



in summer 



14 



Proposals for correcting the calendar had been submitted to 
Pope Paul III (1534-49) and were discussed at the Council of Trent, 



13 

The current difference between the Julian calendar and the revised 
Gregorian calendar is thirteen days. That difference results in Christmas's being 
celebrated on January 7 (thirteen days after December 25, both dates according to the 
Gregorian calendar) by those still using the Julian calendar; for example, many in 
Orthodox countries, such as Russia. In actuality, what is January 7 on the Gregorian 
calendar is December 25 according to the Julian calendar. 

An example of a solarium that marks the seasons by the sun's shadow has 
been built at the University of Illinois at Urbana-Champaign, situated before the 
Beckman Institute. The shadow cast by the modern obelisk (gnomon) of the solarium 
hits specific fountain markers on the ground at solar noon on each solstice and 
equinox. See also the description of the Solarium/Horologium Augusti project at the 
University of Oregon (Eugene) at http://darkwing.uoregon.edu/~klio/ 
solarium/solarium_project.htm (URL accurate as of December 2004). 



8 ^ Dennis C. Smolarski, S.J. 



but only after Pope Gregory XIII was elected in 1572 was a commis- 
sion established to propose a definitive solution after reviewing the 
various proposals. 15 This commission included Clavius, who built on 
the work of Luigi Lilio (d. 1576). As a result of the work of this 
commission, Gregory XIII issued the bull Inter gravissimas in 1582, 
which reformed the calendar. 16 Since the reformed calendar was not 
universally accepted (particularly in Protestant and Orthodox coun- 
tries), Clavius attempted to justify the computations that formed the 
basis for the papal bull against detractors in his tome Novi calendarii 
Romani apologia [Defense of the New Roman Calendar], published in 
1588 and totaling over eight hundred pages. 17 

Other documents authored or influenced by Clavius show 
someone who saw in mathematics a foundational body of knowl- 
edge that was a key to understanding most other disciplines. In 
contrast to the prevailing academic climate in Italian universities in 
the sixteenth century (more on this below), Clavius wrote, "Since . . . 
the mathematical disciplines in fact require, delight in, and honor 
truth . . . there can be no doubt that they must be conceded the first 
place among all the other sciences/' 18 This praise is similar to the 
well-known statement of famed German mathematician Carl Fried- 
rich Gauss (1777-1855) that "mathematics is the queen of the sci- 
ences," but Clavius lived two centuries earlier. 



15 

Discussion about reforming the calendar had been active for several 
centuries. Roger Bacon (1214-92) submitted his treatise De reformatione calendaris to 
Pope Clement IV in 1267. 

The reform consisted of (1) omitting ten days in October 1582, so that 
October 4 was followed by October 15, and (2) modifying the "leap-year rule" so that 
century years not divisible by four hundred were not to be leap years (e.g., 1900, 
2100). 

Details about the reform of the calendar and the role of Clavius may be 
found in Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to 
Commemorate Its 400th Anniversary, 1582-1982, ed. George V. Coyne, M. A. Hoskin, 
and O. Pedersen (Vatican City: Pontificia Academia Scientiarum, Specola Vaticana, 
1983). 

18 

Peter R. Dear, Discipline and Experience: The Mathematical Way in the Scientific 
Revolution (Chicago: The University of Chicago Press, 1995), 38, quoting from "In 
disciplinas mathematicas prolegomena" as follows: "Cum . . . disciplinae mathematical 
veritatem adeo expetant, adament, excolantque, . . . quin eis primus locus inter alias 
scientias omnes sit concedendus" (Christopher Clavius, Opera mathematica [Mainz, 
1611-12], 1:5). 



Jesuits on the Moon ^ 9 

In two documents, most probably written for the Jesuit com- 
mission charged with composing the Ratio studiorum, Clavius de- 
scribes mathematics as being a magnum ornamentum ("great orna- 
ment'' [or "jewel"] in the sense of being an object of honor, pride, 
and distinction rather than meaning an unnecessary embellishment) 
for the Society. 19 He then also argues that all Jesuits should study 
mathematics and that special academies ought to be established 
where scientifically gifted Jesuits could be trained in more depth in 
the mathematical sciences. 

A major contribution of Clavius to the mathematical commu- 
nity of later generations was his set of texts. One example was his 
1574 Elements of Euclid, which was not simply a translation, but a text 
containing Euclid's work as well as a commentary. Some comments 
were taken from earlier authors, but the book also included Clavius's 
own criticisms and elucidations of Euclid's axioms. This text has been 
held up as a model and led to Clavius's being called the "Euclid of 
the Sixteenth Century." 20 

Matteo Ricci 

Perhaps of all the Jesuits who have studied various mathemat- 
ical sciences and have made use of their scientific expertise to help 
spread the Gospel message, the early Chinese missionary Matteo 
Ricci (1552-1610), along with his successors, Johann Adam Schall von 
Bell and Ferdinand Verbiest, deserves special mention. 

Ricci entered the Society in Rome in 1571 and studied mathe- 
matics under Clavius until 1577, when he asked to be sent on mis- 
sion to Asia. Ricci's life is a wonderful example of someone eager to 
learn from the culture in which he found himself, sensitive to that 
culture, and willing to adapt his European mind-set to Chinese 
customs to gain credibility. Ricci (or Li Ma Tau in Chinese) was 
esteemed by the Chinese for his scientific skills as well as his mem- 



19 

The Institute of Jesuit Sources is about to publish a bilingual edition (Latin 
and English) of the Ratio studiorum, the first translation into English of the entire 
Official Ratio of 1599.— Ed. 

20 

Charles C. Gillispie, ed., Dictionary of Scientific Biography (New York: 
Scribner, 1970-90), 311. 



10 <0> Dennis C. Smolarski, S.J. 




Matteo Ricci, S.J. (1552 - 1610) 

ory and his grave in Beijing is still a place of pilgrimage. 21 As is 
widely known, he eventually adapted his manner of dress to that of 
the mandarin class, and his modus operandi of discussing mathe- 
matical and scientific matters first and only afterwards raising issues 
of religion (as noted earlier) shows a very concrete way of following 
Ignatius's counsel of "entering by their door." 

Ricci continued an active correspondence with his former 
teacher, Clavius, and after receiving Clavius's Elements of Euclid, 
translated the work into Chinese, giving China its first exposure to 
Western mathematics and its basis on fundamental principles. Ricci 
acknowledged his intellectual dependence on Clavius and presented 
Clavius as the intellectual heir of Euclid. He also presented his 
scientific tradition (from his small Western country) as one based on 
rigor and reason in which there is no unsubstantiated opinion and 
therefore no doubt. This contrasted with the state of science in 
China at that time, where the methodology did not have a good 
basis. 22 

In commenting on the work of the early Jesuit missionary 
effort in China, Gilbert Highet writes as follows: 



21 

Ricci's memory skills are the subject of Jonathan D. Spence's book The 
Memory Palace of Matteo Ricci (New York: Viking Penguin, 1984). Also see Vincent 
Cronin's The Wise Man from the West (Garden City: Image Books, 1957). 

Cf. Spence, ibid., 143^6. 



Jesuits on the Moon -b 11 



The Jesuits went to unparalleled lengths and showed unbelievable 
patience in adapting themselves to the people they had determined 
to teach. . . . The Jesuits therefore spent several years learning Chi- 
nese philosophy, art, and literature, making ready to meet the 
Chinese on their own level. . . . Instead of being rejected as foreign 
barbarians, they were accepted as intelligent and cultivated men. . . . 
The next stage, which they approached very, very delicately, was to 
make the mandarins willing to learn from them. They did this by 
discussing astronomy with the Chinese scientists, constructing maps 
of the world with the place-names shown in Chinese characters and 
the Chinese empire at the center, presenting sundials and astronomi- 
cal instruments to the high officials whom they met, and ultimately 
by assisting the Imperial Board of Rites to correct its calendar so as to 
forecast eclipses and calculate celestial phenomena more accurately 
than any Chinese had ever been able to do. 23 

Nine years after Ricci's death in 1610, Johann Adam Schall 
arrived in China to continue the work Ricci had begun, and his skill 
in predicting a lunar eclipse led to his being named the director of 
the Chinese Bureau of Astronomy. 24 Unfortunately, at the death of 
the Emperor, Schall was accused of sorcery by rival Chinese astrono- 
mers, but was exonerated of the accusations after his death. While 
being investigated, he had a stroke which left him paralyzed. Schall 
was succeeded by Ferdinand Verbiest, who also succeeded Schall as 
head of the calendar office. Modras notes: 

Verbiest tutored the new emperor in mathematics, introduced the 
thermometer into China, built new astronomical instruments, and in 
the course of the above became the emperor's friend. Thanks to the 
trust and admiration Verbiest inspired, the emperor issued an edict 
in 1692 comparable to the Emperor Constantine's fourth-century 
edict of Milan, which legitimized Christianity for the Roman Empire. 
The Kangxi emperor declared that Christians, no less than Buddhists, 
had a rightful place in Chinese society and culture. (120) 



^Gilbert Highet, The Art of Teaching (New York: Knopf, 1954), 222 f., as 
quoted in Jesuit Geometers, by Joseph MacDonnell, S.J. (St. Louis: The Institute of 
Jesuit Sources, 1989), 63. 

24 

Modras, Ignatian Humanism, 118. 



12 ^ Dennis C. Smolarski, S.J. 



Francois d'Aguilon 

Clavius's vision of a special "academy" to train Jesuit mathe- 
maticians became realized near the end of his life through the efforts 
of Frangois d'Aguilon (1567-1617). D'Aguilon was born in Brussels, 
entered the Society in 1586, and was ordained in 1596. In 1611 he 
founded a school for mathematics in Antwerp and around 1616 was 
joined by Gregory St. Vincent (1584-1667), who had studied under 
Clavius in Rome. During their lives, d'Aguilon focused on geometri- 
cal optics, publishing in 1613 his major work, Six Books of Optics, 
Useful for Philosophers and Mathematicians Alike, and St. Vincent re- 
searched mathematical concepts we would now see as precursors to 
the infinitesimal calculus. Although d'Aguilon's contributions in no 
way compare to the impact of Clavius or Ricci, his role in establish- 
ing a special school for mathematics shows the commitment of the 
early Society to training Jesuits during a time of rapid developments 
in scientific fields. 



III. Mathematics, the Early Society of Jesus, 
and the Ratio studiorum 

The Constitutions gives a general norm about what should be 
taught in Jesuit universities: "Since the end of the learning 
which is acquired in this Society is with God's favor to help 
the souls of its own members and those of their neighbors, it is by 
this norm that the decision will be made ... as to what subjects 
[Jesuits] ought to learn" (ConsCN C 351 v2 ). Elsewhere, we find this 
advice: "Since the arts or natural sciences . . . are useful for the 
perfect understanding and use of [theology], and also by their own 
nature help toward the same ends, they should be treated with 
fitting diligence" (C 450 vl ). 

When the Constitutions list specific subjects taught in universi- 
ties, it says, "Logic, physics, metaphysics, and moral philosophy 
should be treated, and also mathematics, with the moderation 
appropriate to secure the end which is being sought" (C 451 vl ). The 
Latin reads "et etiam mathematics" and, as noted earlier (see n. 2 
above), the presence of the etiam (translated either as "also" or 
"even" in English) seems to give an added emphasis, as if one would 



Jesuits on the Moon <& 13 



not normally expect mathematics to be taught at the university level 
(and, in fact, in most places it was not taught — see below). 

The thrust of Ignatius's thought seems obvious: Any discipline, 
including mathematics and other scientific and technical disciplines, 
which "help[s] souls" is worthy of study in a Jesuit university. This is 
particularly true of those disciplines that "by their own nature help 
toward the . . . ends" envisioned in the Constitutions. 25 

Part IV of the Constitutions also refers to a "separate treatise" to 
be written regarding schools (C 455 vl ), and the Ratio studiorum was 
that document. From a modern perspective, the Ratio was a combi- 
nation of core curriculum guidelines, faculty handbook, and peda- 
gogical manual. As such it is about 

as exciting to read as are some ^^^^^^^^^^^^^^^^^^ 
modern curriculum guidelines and 

faculty handbooks. The Ratio ex- Here the proposed rules for 

panded upon the relatively brief provincials included an 

notes in the Constitutions about exhortation to make sure that 
subjects to be taught and the ped- the college administrators 

agogical methods to be used in took care that the instructors 
Jesuit schools. of philosophy not disparage 

In actuality, several different the di g™ty of mathematics. 

versions of the Ratio were pub- This ^fe concludes with this 
lished by the Curia of the Society: astute observation: "[¥]or it 

two preliminary (and published) often happens, that the less 

drafts in 1586 and in 1591, and the one knows about such things, 
definitive version of 1599. In addi- the more he disparages them." 

tion, a slightly revised version of 
the 1586 text was drafted but 

never published. 26 Neither of the 1586 documents was a first draft; 
both had had several predecessors, the best known of which was the 
Ratio of Francis Borgia, compiled between 1565 and 1572. After the 
preliminary drafts of the Ratio were distributed and discussed, on 
January 8, 1599, fifty-nine years after the papal approbation of the 



25 

Dennis C. Smolarski, S.J., "GC 34, Higher Education, and Computer 
Science," in Promise Renewed: Jesuit Higher Education for a New Millennium, ed. Martin 
R. Tripole, S.J. (Chicago: Loyola Press, 1999), 109 f. 

26 

The second 1586 version was recently found in the Jesuit archives. See 
Frederick A. Homann, S.J., Church, Culture, and Curriculum: Theology and Mathematics 
in the Jesuit "Ratio Studiorum" (Philadelphia: St. Joseph's University Press, 1999), 34. 



14 <t Dennis C. Smolarski, S.J. 



Society of Jesus and forty-three years after the death of St. Ignatius, 
the definitive version of the Ratio studiorum was approved. 27 

The Ratio was influenced by various dynamics in the late- 
sixteenth century, including the academic climate in Italy, the na- 
scent scientific revolution, and the practices of the Roman College 
along with the experiences of its faculty, including Clavius (and his 
experiences in helping to revise the calendar). Reviewing these three 
dynamics, in particular, may help the reader better understand some 
of the guidelines contained in the definitive Ratio, and better appre- 
ciate the evolution of the text that culminated in the 1599 Ratio. 

Academic Climate in Italy 

To appreciate more fully what the Ratio says about mathemat- 
ics, it is important to read the various drafts of the Ratio in light of 

the lack of prestige given in the 
— — ^ — sixteenth century to mathematics 
He saw the intrinsic and and to what we would now call 

apostolic value of scientific and technical disciplines. 

mathematics and, as noted At that time ' a number of Italian 

above, did not share the philosophers, including some Jesu- 

opinion of some of his "?' denied r t0 . P ure mathemati f 

.. „ 7 the status of scientia, true scientific 

university colleagues who t , , . A . 

m i x- i i i knowledge in Aristotle s sense, 

gave it a relatively low place . ,f ,., t , 

. a7 , . i r j . because it did not demonstrate its 
in the hierarchy of academic , . ., , _, . 

,. . .. J J conclusions through causes and it 

" ' dealt with abstractions in the intel- 

________ lect, rather than real objects. 28 

Thus, mathematics was not con- 
sidered by many to be worthy of study in a university. Mathematics 
was presented via the subjects of the quadrivium, namely, arithme- 
tic, geometry, music (taught as applied arithmetic), and astronomy 



27 

This definitive 1599 Ratio appeared at a crucial time in the growth of Jesuit 
schools, for in 1556, at the death of Ignatius, Jesuit schools numbered about 35, but 
forty years later, in 1596, they numbered around 245. Then, nineteen years later, in 
1615, three years after the death of Clavius and sixteen years after the promulgation 
of the Ratio, they numbered around 372 (see Martin P. Harney, S.J. The Jesuits in 
History: The Society of Jesus through Four Centuries [New York: America Press, 1941], 201). 

28 

Dear, Discipline and Experience, 36 f.; Homann, Church, Culture and 
Curriculum, 5; Wallace, Galileo and His Sources, 136. 



Jesuits on the Moon -& 15 



(taught as applied geometry), and also, in some degree, via logic 
(one subject of the trivium). But at that time the trivium and quad- 
rivium were considered preparatory arts studied before one pursued 
the higher disciplines of theology, medicine, or law, which were 
usually the only accepted disciplines for university study, particu- 
larly in Italy. 29 

We should also note that the "mathematical sciences'' in the 
sixteenth century included applied topics now considered separately 
as part of astronomy, physics, and engineering and that "physics" 
usually meant the philosophy of nature. 30 

The tension between those who saw value in mathematics 
being taught in a university and those who did not is evident in the 
1591 draft of the Ratio. Here the proposed rules for provincials 
included an exhortation to make sure that the college administrators 
took care that the instructors of philosophy not disparage the dignity 
of mathematics. This rule concludes with this astute observation: 
"[F]or it often happens, that the less one knows about such things, 
the more he disparages them." 31 People waxing eloquent about 
subjects they know little about is not a new phenomenon in human 
history. The tension also is seen in an earlier document written by 
Clavius (noted below) which recommends that instructors of mathe- 
matics be invited to solemn academic assemblies (when decrees are 
conferred) and be involved in public disputations. The document 
then comments, "[S]ince up to now the students seem almost to 
have despised these [mathematical] sciences for the simple reason 



29 

Homann, ibid., 81; cf. Dear, ibid., 35. The arts and humanities were only 
beginning to make their way into the universities, to be followed by the sciences as 
we think of them today. 

30 

See the introduction by Edward C. Phillips, S.J., to the translations of 
Documents 34 and 35 (of Clavius): "For a better understanding of some portions of 
these documents, it should be remembered that at that period 'Mathematics' was a 
term including astronomy and much of what would now be taught in physics" 
(Bulletin of the American Association of Jesuit Scientists [Eastern Section]) 18, no. 4 [May 
1941]: 203). Also, see Homann, Church, Culture and Curriculum: "Mathematics courses 
comprised not only arithmetic, geometry, and algebra, but also diverse use of 
mensuration and calculus in astronomy and astrology, computation of time (calendar 
and sundial), surveying, theory of music, optics (perspective), and mechanics" (81). 

31 

"Fit enim saepe, ut qui minus ista novit, his magis detrahat" ("Regulse 
Propositi Provincialis: 'De mathematicis,'" in the 1591 Ratio studiorum, no. 44; see 
Homann, ibid., 79n69. 



16 ^ Dennis C. Smolarski, S.J. 



that they think that they are not considered of value and are even 
useless, since the person who teaches them is never summoned to 
public events with the other professors/' 32 

The Nascent Scientific Revolution 

It seems also important to situate the 1599 Ratio among the 
significant events in the history of science. In 1543 Nicholas Coperni- 
cus published De revolutionibus orbium ccelestium [On the Revolutions 

of the Heavenly Spheres], and in 
1582 Pope Gregory XIII ordered 
Clavius bemoaned the the shift to the Gregorian calen- 

poverty of mathematical dar. Later, in 1633, Galileo's thesis 

interest and instruction, and was condemned; 33 and in 1687, Sir 
argued that the lack of well- Isaac Newton published his Philo- 

trained mathematics teachers S0 P hia naturalis principia mathematica 
and the absence of Jesuits [Mathematical Principles of Naru- 

studying mathematics ral Philosophy]. The Ratio ap- 

harmed the Society. P eared about the same time as the 

beginnings of the scientific revolu- 

— ^ — ■ tion, and although references to 

mathematics and sciences are rela- 
tively few, what it did contain did influence the teaching of mathe- 
matics and science in Jesuit schools for generations at an important 
moment in the history of science. 

The Influence of Clavius on the Ratio studiorum 

Clavius realized the important role mathematics played in 
revising the calendar (1582) and, through his correspondence with 
Ricci in China (after Ricci left Rome in 1577), also knew that mathe- 
matics could be the doorway through which Western culture and 
science as well as faith in Christ could be brought to other peoples 
and cultures. He saw the intrinsic and apostolic value of mathemat- 
ics and, as noted above, did not share the opinion of some of his 



32 

For the complete text, see Christopher Clavius, S.J., "Historical Documents, 
Part II: Two Documents on Mathematics," Science in Context 15, no. 3 (Sept 2002): 
465-70. 

33 

In Galileo and His Sources, Wallace shows an exchange of idea between 
Galileo and Clavius at the Roman College (pp. 91, 269). 



Jesuits on the Moon <& 17 



university colleagues who gave it a relatively low place in the hierar- 
chy of academic disciplines. 

Although not officially a member of any commission involved 
with the Ratio, Clavius's influence on the Ratio's sections on mathe- 
matics cannot be denied. 34 Around 1580, Clavius authored two 
documents, probably written for the commission charged with 
composing the first version of the 1586 Ratio. 35 Similarities between 
the sentiments expressed in these documents and in the 1586 and 
1591 drafts of the Ratio along with 
the inclusion of Clavius's name in "" """" ~ ~ " " — — 
these drafts attest to their influ- He wanted to make sure that 
ence (see Appendix 2 for excerpts Jesuit schools placed proper 

from the 1586 Ratio). emphasis on mathematics by 

rn r. , , , , recruiting and training 

The first document, Modus ..... f. A A ° 

j. . 7 . , r .. , ,. qualified instructors of 

quo discipline mathematics in scholis J J . »* * 

c • . .. • . • rA a>t-u mathematics as well as by 

bocietatis vossint vromoveri [A Mem- . u 

od of Promoting the Mathematical requiring that mathematics 

Disciplines in the Schools of the be studted h V alL 

Society], 36 blamed philosophy in- ^^^^^^^^^^^^_^_^^^ — 
structors, in part, for the low opin- 
ion held by many about mathematics because some "teach that 
mathematical sciences are not sciences" and that they do not have 
proofs. 37 Clavius bemoaned the poverty of mathematical interest and 
instruction, and argued that the lack of well-trained mathematics 
teachers and the absence of Jesuits studying mathematics harmed 
the Society. 38 The document also notes that without mathematics one 



34 

In an article by Gabriel Codina, S.J., Clavius's name does not appear among 
the members of any commission charged with writing or revising various drafts of 
the Ratio. Cf. Gabriel Codina, S.J., '"Our Way of Proceeding' in Education: The Ratio 
Studiorum," Educatio S.J., no. 1 (May 1999): 8f. 

35 

Homann, Church, Culture, and Curriculum, 61, 64. 

36 

This is Document 34 in the 1901 Monumenta Paedagogica S.I., found as well in 
vol. 7 of the 1992 Monumenta Paedagogica S.I., "Collectanea de Ratione Studiorum 
Societatis Iesu," 109-22. A translation of this document and of Document 35 is found 
in Science in Context 15, no. 3 (2002): 465-70. 

37 

Homann, Church, Culture, and Curriculum, 61 f.; Dear, Discipline and 
Experience, 35; Clavius, "A Method . . . ," (Doc. 34; 1901 Latin text): "praeceptores 
philosophicae ... in quibus docent scientias mathematicas non esse scientias" (p. 473). 

38 

Homann, ibid., 61 f. 



18 <$- Dennis C. Smolarski, SJ. 



cannot understand most physical phenomena. 39 He then proposes 
establishing a special "private academy" for Jesuits to study mathe- 
matics. 

Now in order that the Society may be able always to have capable 
professors of these [mathematical] sciences, some men apt and 
capable of undertaking this task ought to be chosen who may be 
instructed in a private academy in various mathematical topics; 
otherwise it does not seem possible that these studies will last long 
in the Society, let alone be promoted; since, however, they are a 
great ornament to the Society, and quite frequently a discussion 
about them will occur in conversations and meetings of leading men, 
where they might understand that Ours are not ignorant of mathe- 
matical topics. 

Clavius's other brief note, De re mathematica instructio [On 
Teaching Mathematics], dealt with faculty problems and the need to 
have well-trained, mature instructors. 40 Its sentiments influenced the 

1586 Ratio, which prescribes teach- 

— ^^^^^^^— ^^^^^^— ^— ers of mathematics in gymnasia 

Some modern scholars view and at least *"° mathematics in- 

the 1586 Ratio as a radical structors at the Roman College, 

j . £ . . naming Clavius as a possibility for 

document for raisin? /> ... 

x7 / , ° one of these positions. 

mathematics to be on a par r 

with other university-level From his work with the cal " 

disciplines and for giving it a endar-revision commission, Clavi- 
prominence unheard of in us ' s influence may also be seen in 

Italian universities. the statement in the 1586 R «[ 10 

that if one or two people leave the 

— «^— — -^— ^^^ Roman College, there may not be 

anyone left who can "be at hand 

for the Apostolic See, when there is a discussion about ecclesiastical 

times" (1586 Ratio, "De mathematicis," no. 1). His knowledge about 

Ricci's missionary efforts may have given rise to the suggestion of 



39 

Homann, ibid., 62; Clavius, ibid., (Doc. 34; 1901 Latin text): "cum tamen 
apud peritos constet physicam sine illis recte percipi non posse" (p. 472). Some of the 
thrust of this apologia for mathematics seems to have influenced the content of the 
1586 Ratio if not the exact wording as well. 

This is Document 35 in the 1901 Monumenta Peedagogica S.I. A translation of 
this document and of Document 34 is found in Science in Context 15, no. 3 (2002): 
465-70. See Homann, Church, Culture and Curriculum, 63. 



Jesuits on the Moon <& 19 



establishing an academy of eight to ten Jesuits to study specialized 
mathematics, and the comment, " Afterwards, the excellent mathema- 
ticians of this academy will go forth, who will disseminate this 
discipline into all provinces to which they will return, and they will 
uphold the reputation of Ours, if at any time it behooves them to 
speak about mathematics" (1586 Ratio, "De mathematicis," no. 3). 41 

The impact Clavius had on the 1586 Ratio cannot be overesti- 
mated. He was someone who had done significant scientific and 
mathematical work; his effort in revising the Julian calendar noted 
earlier was just one example. 42 And he proclaimed the importance of 
mathematics in the face of an academic culture in Italy and professo- 
rial colleagues at the Roman College who apparently demeaned 
mathematics whenever possible. Clavius saw new uses for mathe- 
matics in ways that were only beginning to be discovered in the last 
decades of the sixteenth century. He wanted to make sure that Jesuit 
schools placed proper emphasis on mathematics by recruiting and 
training qualified instructors of mathematics as well as by requiring 
that mathematics be studied by all. Clavius's daring proposals are 
now viewed by some as revolutionary. He did not want partial 
remedies but a complete and complex strategy to obtain a radical 
change in attitude and structures. 43 It was probably due to Clavius's 
influence that the 1586 Ratio included a lengthy apologia about 
mathematics and its connection to various disciplines and profes- 
sions, including poetry, history, politics, metaphysics, theology, law, 
farming, and medicine. More concretely, the 1586 Ratio required all 
students to take mathematics for at least a year and a half (1586 
Ratio, "De mathematicis," no. 2). 

Some modern scholars view the 1586 Ratio as a radical docu- 
ment for raising mathematics to be on a par with other university- 



Cf. Rivka Feldhay, Galileo and the Church: Political Inquisition or Critical 
Dialogue? (Cambridge: Cambridge University Press, 1995), 221 f. 

42 

We should also note some of Clavius's other contributions to mathematics, 
such as the use of x as an indeterminate unknown quantity (Florian Cajori, A History 
of Mathematical Notations, vol. 1, Notations in Elementary Mathematics [LaSalle, 111.: The 
Open Court Publ. Co., 1928], 154, §161 and MacDonnell, Jesuit Geometers, 29; the 
decimal point (Cajori, ibid., 322, §280; MacDonnell, ibid., 18); parentheses in algebraic 
expressions (Cajori, ibid., 151, §161, 392, §351; MacDonnell, ibid., App. 1, p. 5 [p. 5 of 
the appendix section is toward the rear of the book]). He seems to be one of the first 
in Italy to make use of the square-root sign (Cajori, ibid., 369, §327). 

43 T 
Homann, Church, Culture, and Curriculum, 64; Feldhay, Galileo and the Church, 221. 



20 <0> Dennis C. Smolarski, S.J. 



level disciplines and for giving it a prominence unheard of in Italian 
universities. 44 Clavius's insight about the importance of the mathe- 
matical sciences, especially as incarnated in the 1586 Ratio, provides 
us with a vision about mathematical (and other contemporary 
technical) disciplines, their importance for understanding our world, 
and their usefulness in our ongoing quest to find God in all things 
and to proclaim God's presence in a world still searching for him. 
Unfortunately, the culture and the times of the sixteenth century 
were not appropriately receptive to this insight. 



The Evolving Ratio studiorum 

In the early 1580s, the creation of the Ratio studiorum was 
authorized by Father General Claude Aquaviva in order to provide 
common guidelines for the curriculum, pedagogy, and organization 
of the increasing number of Jesuit schools in Europe and elsewhere. 
In 1584 six Jesuit university instructors, elected from different Euro- 
pean Jesuit provinces, gathered in 
— ^^— ^^— ^^^^^ Rome and reviewed the various 

The 1586 first draft of the loc * 1 education documents in use 

t, .. j s. Ji r at Jesuit schools. In August 1585 

Ratio seemed too radical for ' . ..? , 

. j. ., , T J this commission submitted a re- 

some individuals. In . . , 

aT . , - port to Aquaviva, who, in turn, 

response, this draft was r . ,. , ^ u , r. . .%, , ,. 

; . ', , * . , submitted the draft to the faculty 

submitted by a Spanish rf ^ Roman CoU where Qa _ 

Jesuit, Father Enrique vius had been teaching for some 

Ennquez, to the Spanish ^ eniy years « Mter revision/ the 

Inquisition. first draft of the Ratio a pp earec i i n 

«—^ m ^^ m ^^ mm ^^^ 1586 and was sent to Jesuit schools 

throughout Europe with a request 
for comments. As noted earlier, a second draft ("1586B") also was 
written in 1586 but was not published or circulated. The collected 
comments on the original 1586 Ratio were again studied by the 
faculty of the Roman College (including, presumably, Clavius) and a 
revised Ratio was published in 1591 to be circulated for review. After 
more study in Rome, both by Father General Aquaviva and the 



Feldhay, ibid., 221 f.; Dear, Discipline and Experience, 35. 

45 

E. Fitzpatrick, ed., St. Ignatius and the "Ratio Studiorum" (New York: 
McGraw-Hill Book Co., Inc., 1933), 28-30. 



Jesuits on the Moon -$- 21 



faculty of the Roman College, a definitive version was promulgated 
in 1599. 46 (Also see the introductory letter promulgating the 1599 
Ratio.) 47 

The 1586 first draft of the Ratio seemed too radical for some 
individuals. In response, this draft was submitted by a Spanish 
Jesuit, Father Enrique Enriquez, to the Spanish Inquisition. His 
contention was that the Ratio was at variance with the teachings of 
St. Thomas Aquinas, much of whose outlook was Aristotelian. 48 
Changes were introduced into the Ratio, and some of the differences 
between the 1586 draft and the definitive 1599 Ratio are noteworthy 
in light of analyses by contempo- 
rary scholars. 49 One striking differ- ^ — 
ence pertains to the amount of One could rightly wonder 

text devoted to mathematics. In whether the 1599 Ratio 

the 1599 Ratio, the references to represents a retreat from the 

mathematics are only about a intense interest in 

quarter of the length of what is mathematics evident in the 

found in the first 1586 draft. 1586 draft 



The never-published 1586 1 ^^^^___ - __ - _ - 
second draft kept the apologia for 

mathematics found in the first draft, but revised the practical advice. 
This new draft added a public presentation of mathematical prob- 
lems before an assembly of students once or twice a month, and 
monthly repetitions of the principal topics in an interactive format. 
In contrast, the number of students mentioned for special tutoring is 
reduced from eight or ten to only four or five. (Maybe the revisors 
of the Ratio felt that Clavius was too optimistic in gauging the 
number of Jesuits competent to study advanced mathematics.) 



46 

Fitzpatrick, St. Ignatius and the "Ratio Studiorum," 31-33. 

Ibid., 119 f., and Farrell's translation of the Ratio studiorum, xii-xiii, available 
at www.bc.edu jDrg/avp/ulib/digi/ratio/ratiohome.html 

Farrell, ibid., 231; Feldhay, Galileo and the Church, 222. 

49 Cf. Feldhay, ibid., 223ff. 

50 

In the first 1586 version, the section dealing with mathematics runs to about 
fifty-four lines in a recent edition of the Latin text. In the 1599 version, the section 
dealing with mathematics is only ten lines in the same edition, with four additional 
lines about studying mathematics in a different section. 



22 <0> Dennis C. Smolarski, S.J. 



The 1591 draft did not include any rationale as to why various 
disciplines were to be taught. So the general apologia for mathemat- 
ics disappeared. In addition, the study of mathematics by all is 
reduced to one year. A second year is only recommended for stu- 
dents of metaphysics, and the length of time for private tutoring is 
reduced from three years to six months. 51 

The definitive 1599 Ratio (see excerpts in Appendix 3) makes 
no direct mention of how long students should study mathematics, 
but only says that mathematics should be taught to the students of 
physics and those in the second year of philosophy. It also reduced 
the public presentations of mathematical problems from once or 
twice a month to each month or every other month. 

One could rightly wonder whether the 1599 Ratio represents a 
retreat from the intense interest in mathematics evident in the 1586 
draft. In a sense, it does, yet one should not overlook the fact that 
the definitive text is overall a much leaner document than the earlier 
drafts (hence the absence of anything like the 1586 apologia). In 
addition, mathematics is still required in Jesuit schools (unlike in 
most other Italian universities of the period), along with regularly 
scheduled public presentations of mathematical problems. This 
commitment to mathematics is still noteworthy in the history of 
higher education. 

IV. The Definitive 1599 Ratio studiorum 
and the Revised Ratio of 1832 

The 1599 Ratio served newly established Jesuit schools well. 
Over the years, mathematicians and other scientists, Jesuit 
and non-Jesuit, well known and obscure, all benefited from 
the approach taken toward mathematics and science in Jesuit institu- 
tions. Over the approximately two centuries between the publication 
of the Ratio and the suppression and restoration of the Society, 
however, the world changed significantly. And even though the 
Ratio was adapted in various ways, based on the Ignatian principle 



The philosophy curriculum at the Roman College in the late-sixteenth 
century consisted of a three-year cycle, with logic taught the first year, natural 
philosophy and mathematics the second, and metaphysics the third. See Wallace, 
Galileo and His Sources, 6-8, 59-61. 



Jesuits on the Moon <$> 23 



of adapting to persons and places as found in the Constitutions and 
the Spiritual Exercises, for various reasons 52 (the primarily ones being 
the suppression of the Society, the rapid development in the sci- 
ences, and the political upheavals in various parts of the world in 
the late 1700s and early 1800s) the impact of the original Ratio 
regarding mathematics and science generally seems to have dissi- 
pated over two centuries. 

Father General Luigi Fortis (the second general after the 
restoration of the Society), with a mandate from the general congre- 
gation that elected him, started a revision of the Ratio studiorum. He 
appointed a commission and solicited opinions about educational 
needs in a post-French Revolution 
world. As William Bangert, S.J., 
notes, "Many reports indicated 

new trends: greater attention to Over the years, 

vernacular languages; wider stress mathematicians and other 

on mathematics, history, and ge- scientists, Jesuit and non- 

ography; a more alert appreciation Jesuit, well known and 

in logic and metaphysics of mod- obscure, all benefited from the 
ern philosophical currents; a com- approach taken toward 

prehensiveness in projecting a mathematics and science in 

program for the natural sci- Jesuit institutions. 

ences." 53 After Fortis's death in 

1829, Father General Jan Roo- 

thaan, with a new mandate from 

the next general congregation, issued in 1832 a revised Ratio on a 
trial basis, but this version never received the approbation of any 
general congregation. The 1832 Ratio was not an extensive revision; 
it did, however, explicitly permit the study of vernacular literature, 
and one of the new rules for the professor of physics notes the 
obligation of the instructor to keep up to date because of the new 



52 

For example, we find the following in the Constitutions: "[The separate 
treatise on schools] ought to be adapted to places, times, and persons" (C 455 v3 ); 
"that which is found to be more suitable may be done" (C 477); "These details and 
those which follow below are appropriate and should be observed when possible, 
but they are not necessary" (C 526 vl ). In the Spiritual Exercises we also read, "The 
Spiritual Exercises must be adapted to the condition of the one who is to engage in 
them, that is, to his age, education, and talent" (18 vl [pp. 26 f.]). 

53 

William V. Bangert, S.J., A History of the Society of Jesus, 2nd ed. (St. Louis: 
The Institute of Jesuit Sources, 1986), 435-37. 



24 <$> Dennis C. Smolarski, S.J. 



advances in science every day. Yet the political realities of that era 
(revolutions in the United States [1776], France [1790], Paraguay 
[1811], Spain [1820], Mexico [1810-1820], Austria, Hungary, and 
Germany [1848], among others) impacted the possibility of ever 
having a unified, worldwide Ratio. The new governments often 
made education one of their specialized interests, superseding 
anything a revised Ratio would contain. In addition, the 1832 Ratio 
contained only a few accommodations to the rapidly changing 
educational landscape, not taking the contemporary educational 
currents sufficiently into account. Compared to its 1599 ancestor, the 
1832 Ratio was a case of "too little, too late/ and the attempt to 
reclaim the glory of the earlier Ratio ended more with a whimper 
than a bang. 54 

V. Reflections 

The world is a significantly different place now than it was 
when Clavius was defending the new calendar, Ricci was 
translating Clavius's text on Euclid into Chinese, and the 1599 
Ratio was promulgated. Since that time, entire areas of mathematics 
and science have been developed and have even been taken for 
granted. When I began my undergraduate studies as a mathematics 
major in 1965, 1 was worried that I would not get the correct type of 
slide rule. Today, most incoming college freshmen arrive on campus 
with their own computers (occasionally several) and have spent 
several years using e-mail and looking up information via Google on 
the Internet. But one can rightly wonder how well the avalanche of 
information, both technical and nontechnical, available via comput- 
ers has drawn students closer to God or, at the least, raised ques- 
tions about the use of science and technology for the benefit of 
human society. In an often quoted passage, T. S. Eliot, in his cho- 
ruses from The Rock, poses some crucial questions about the purpose 
of knowledge: 

The endless cycle of idea and action, 

Endless invention, endless experiment, 

Brings knowledge of motion, but not of stillness; 



Codina, " 'Our Way of Proceeding' in Education," 15; John W. Donohue, S.J., 
Jesuit Education: An Essay on the Foundations of Its Idea (New York: Fordham University 
Press, 1963), 53. 



Jesuits on the Moon $ 25 



Knowledge of speech, but not of silence; 
Knowledge of words, and ignorance of the Word. 

All our knowledge brings us nearer to our ignorance, 

All our ignorance brings us nearer to death, 

But nearness to death no nearer to God. 

Where is the Life we have lost in living? 

Where is the wisdom we have lost in knowledge? 

Where is the knowledge we have lost in information? 55 

To my mind, one special charism of the Society of Jesus and its 
scholarly tradition has been the ability of Jesuits to start with infor- 
mation of various sorts and let that information draw them nearer to 
the knowledge of God, as the Society pursues "what will seem 
expedient for the glory of God and the common good." 56 

Having reviewed the history of the Society's involvement in 
mathematics (and other scientific and technical fields) in the earlier 
sections, I would now like to offer some personal reflections on how 
mathematical information has, in fact, drawn me "nearer to God. " I 
would also like to raise some questions about what the Society's past 
involvement in the mathematical sciences might suggest about our 
future. I admit that it is very easy to raise questions and identify 
problems, but much more difficult to provide answers and solutions. 
Yet often it is more important to ask the question than to provide 
any immediate answer. 

Seeking and Finding God 

Students of literature, music, or art, lacking the ability to 
interview authors, composers, or artists of previous centuries, often 
come to know the "mind" of the artist by examining the various 
artistic creations produced, whether those creations be plays, novels, 
operas, symphonies, paintings, or sculptures. In a similar way, I feel 
I am drawn into ever-deeper insights into the "mind" of God 
through mathematics, in particular when I reflect on the coherence, 
pervasiveness, order, and beauty of my field. In "reading" the book 
of the universe, "written in the language of mathematics" (quoting 
Galileo once again), I am drawn into a deeper awe of the Creator as 



55 T. S. Eliot, The Complete Poems and Plays, 1909-1950 (New York: Harcourt, 
Brace and World, 1952). 

56 "Formula of the Institute/' in ConsCN l vj (p. 4). 



26 <f Dennis C. Smolarski, SJ. 



I marvel at* the wonders of creation. And then, standing in awe 
before my loving God, I also feel drawn more into my academic 
discipline, to come to a deeper understanding of the works of 
creation. I think my feelings are shared by other scientists who are 
also individuals of faith. I remember reading an article, years ago, by 
someone who was reflecting on the wonders of computers (then just 
becoming more and more widespread), and how a combination of 
silicon chips, disk drives, and connecting wires could do so much. 
The author then paused, as it were, and reflected that, even though 
the personal computer was amazing, even more amazing were the 
human minds that created the computer. For me, it is when I look at 
the mathematical "laws" that are used in so many ways to describe, 
albeit often imperfectly, the motion of the planets, the growth of 
population, the power of earthquakes, and so on, that I continue to 
stand in awe of my God, whose love brought such order out of the 
chaos of the primordial sea. 

I do not see myself so much as bringing order out of chaos as 
attempting to see the order and patterns that exist in God's creation 

and then describing and interrelat- 
^ — ^^^^^^^— ing these patterns using the sym- 
Mathematics can help train bols of mathematics. Over the 

individuals to think years, I have been struck by the 

abstractly and in disciplined, mathematical patterns that recur 
structured ways, thereby throughout nature, sensing a Di- 

offering them ways to vine Plan in what at times seems 

describe so many aspects of like the chaotic nature of the uni- 

Gods creation. verse. My feelings often mirror 

mm ^^^ mmm ^ mmmm ^ m ^ mm ^^^^^^^ statements by minds much greater 

than mine, such as the statement 
"God exists because mathematics is consistent, and the Devil exists 
because we can't prove it." 57 

Timothy Toohig, S.J., in his essay "Physics Research, a Search 
for God," concluded with a reflection on how his physics research 
was related to his search for God and to an appreciation of the sense 



57 

This statement has been attributed both to Hermann Weyl (1885-1955) and 
to Andre Weil (1906-98) (in Mathematical Circles Adieu, by Howard W. Eves [Boston: 
Prindle, Weber & Schmidt, 1977]). 



Jesuits on the Moon <$■ 27 



of mystery, both of creation and of redemption. 58 In a similar way, 
mathematics draws me to reflect on the wonders of creation, seeing 
connections that are so often overlooked. But since mathematics is 
the "language" of science and technology, I also rejoice at those 
ways that mathematics has assisted other scientists to improve our 
human condition in so many ways, whether by helping meteorolo- 
gists better predict the weather, or helping engineers design stronger 
earthquake-resistant buildings and bridges. 

In recent months I, as possibly many others, found myself to 
be in awe at photos taken by NASA's Hubble Space Telescope of 
galaxies and nebulae at the end of the known universe. 59 While 
looking at the Hubble pictures, I reflected on the ways that comput- 
ers and mathematics have aided other scientists to obtain such 
images and also whether the beauty seen in these patterns can be 
described via mathematical equations. My reflections, in a sense, 
mirrored the first section of "De mathematicis" in the 1586 draft of 
the Ratio that spoke about the interrelation between mathematics 
and other human disciplines (see Appendix 2). 

Mathematics is an abstraction, sometimes even called the 
"science of patterns." For example, what is the numeral "3" other 
than an abstraction that describes the common pattern found in 3 
oranges, 3 dogs, 3 squares, or 3 houses? Or what is the Pythagorean 
Theorem but an abstraction that describes the pattern found be- 
tween the hypotenuse and the other two sides of a right triangle? 
Mathematics can help train individuals to think abstractly and in 
disciplined, structured ways, thereby offering them ways to describe 
so many aspects of God's creation. Although many people today, 
Jesuits included, may exhibit a benign tolerance toward mathematics 
and other related scientific and technical fields (and some may even 
claim to have "math anxiety"), most would also acknowledge the 
underlying importance of mathematics and other technical human 
disciplines. 

Speaking about "beauty" in relationship to mathematics, as I 
did earlier, may seem novel to some readers. I must admit that I, 
too, was surprised when, years ago, as an undergraduate, I read the 



58 

Timothy E. Toohig, S.J., "Physics Research, A Search for God," STUDIES IN 
the Spirituality of Jesuits 31, no. 2 (March 1999): 25 f. 

59 

See hubblesite.org or hubble.nasa.gov for some recent pictures. 



28 <f Dennis C. Smolarski, S.J. 



following in one of my mathematics texts: "It works! Isn't that 
lovely? Such a delightful display of symmetry should make shivers 
of joy run up and down the spine of anyone with any mathematical 
sensitivity. ,,6 ° Yet, even taking into account a bit of poetic hyperbole 
in this statement, it does capture some of the joy and enthusiasm 
that mathematicians feel when doing mathematics. For many mathe- 
maticians, the focus is on the process of doing mathematics, rather 
than on the end product. In addition, for theoretical mathematicians, 
the focus is on the abstract theory as one form of basic scientific 
research, rather than any immediate practical application (although 
often mathematical questions arise from problems raised in some 
other scientific field, like physics, for example. There is an excitement 
in the pursuit of trying to find connections between what may, at 
first glance, seem very disconnected; there is an exhilarated feeling 
when one goes from a hunch that some proposition may be true to 
a detailed, rigorous proof. Often significant mathematical results are 
described as being "deep" and *a particularly well-crafted proof is 
described as "elegant." Such modifying descriptors are more similar 
to words used in the fields of art or music than those used in other 
academic disciplines. 

Bertrand Russell also addressed the beauty of mathematics 
when he wrote, "Mathematics, rightly viewed, possesses not only 
truth, but supreme beauty — a beauty cold and austere, like that of 
sculpture, without appeal to any part of our weaker nature, without 
the gorgeous trappings of painting or music, yet sublimely pure, and 
capable of a stern perfection such as only the greatest art can 
show." 61 

I suggest that it is due to the inner beauty of mathematics, 
albeit not always obvious to many people, as well as due to the 
usefulness of mathematics in so many other human disciplines, that 
the Society has had a long and distinguished history of involvement 
in mathematics and, in the case of Ricci and others, used mathemat- 
ics as a vehicle through which the Gospel message might be spread. 



J. B. Fraleigh, A First Course in Abstract Algebra (Reading: Addison Wesley 



Co., 1967), 92. 

61 Bert 
(London: Longmans, Green & Co, 1910), 73 



Bertrand Russell (1872-1970), The Study of Mathematics: Philosophical Essays 



Jesuits on the Moon *& 29 



The "Desires" and Insights of Clavius 

In both the Constitutions and the Spiritual Exercises, Ignatius 
speaks about desires (ConstSJ, Gen. Exam. [101, 102], in speaking 
about a candidate's "desires"; SvEx [48], in recommending focus for 
the second or third prelude for a meditation, "to ask for what I 
desire"). 62 Ignatius saw in these desires a locus for communicating 
with God. From the various writings of Clavius, we see someone 
who had great "desires" (perhaps better called "passion") about the 
mathematical sciences and was desirous of setting others on fire 
about mathematics itself as well as about its many applications. 

Perhaps it was Clavius's experience with justifying the Grego- 
rian calendar that led him to proclaim the pervasiveness of mathe- 
matics in so many areas of human life and to argue about the 
necessity for Jesuits to learn enough mathematics to feel at ease with 
the logical and technical side of nature. Ricci, who styled himself as 
a disciple of Clavius, was able to present the Greek and European 
mathematical traditions to the people of China as disciplines based 
on logic and reason, which derived mathematical truths from funda- 
mental axioms. Given the years Ricci and Clavius spent together in 
Rome and their subsequent correspondence, it seems plausible that 
Ricci's approach was inspired by Clavius. Since mathematics is based 
on logic alone, it is a system of truths not bound to any sort of 
divine revelation and provides a topic about which individuals of 
different religious traditions, or no religious tradition, can discuss 
starting at a common ground. 

Clavius's insistence on the importance of mathematics also 
suggests to me that he might have had an inkling into the role 
mathematics would play in the world of science, just then beginning 
to expand. Certainly Clavius examined Copernicus's work in his 
efforts to reform of the calendar and is also known to have met with 
Galileo. These insights translated into his insistence that Jesuits be 
well enough grounded in the foundations of mathematics (and the 
various "mathematical sciences") to help guide the path of scientific 
progress in its infancy. 

In fact, Jesuits played a significant role in science in the seven- 
teenth century (when the modern divisions into separate disciplines 



62 

General Examen, in ConsCN lOlf. passim; SpEx 48 vl (p. 40). 



30 <0> Dennis C. Smolarski, S.J. 



were not as clear-cut as they are today and many were highly 
mathematical). We read, for example, that 

[t]he Jesuits had a particular zest for experimental science; they were 
interested in every newly discovered phenomenon, from electrostatic 
attraction to the barometer to the magic lantern, and Jesuits played a 
major role in discovering many new effects on their own, such as 
diffraction and electrical repulsion. A recent history of early electrical 
science awarded the Jesuit order the honor of being the single most 
important contributor to experimental physics in the seventeenth 
century. Such an accolade would only be strengthened by detailed 
studies of other sciences, such as optics, where virtually all the 
important treatises of the period were written by Jesuits. . . . Another 
admirable feature of the Jesuit scientific enterprise was their appreci- 
ation of the value of collaboration. One might well argue that the 
Society of Jesus, rather than the Accademia del Cimento or the Royal 
Society, was the first true scientific society. 63 

Elsewhere we find this evaluation: 

The Society of Jesus in the 17th century contained within its ranks an 
astonishing number of enthusiastic students of the natural world. 
Indeed, for the first sixty years of the century, the Jesuits were the 
only scientific society in existence anywhere. At a time when experi- 
mental science was decidedly unfashionable, Jesuits were charting 
sunspots, calibrating pendulums, timing the fall of weights off tow- 
ers, and devising a variety of ingenious inventions. Indeed, in the 
field of geometry, optics, magnetism, cartography, mechanics, and 
earth sciences, most of the principal authors throughout the century 
were members of the Society of Jesus. The Jesuits were a remarkably 
bold and imaginative scientific body. 64 



Contemporary Jesuit Scientific and Technical Ministries 

Lest it seems that I am overlooking contemporary Jesuit 
involvement in mathematically related sciences and other areas of 
technology, let me acknowledge the work of the Society at the 
Specola Vaticana (Vatican Observatory). Papal support of astronomi- 



63 

David C. Lindberg and Ronald L. Numbers, eds., God and Nature: Historical 
Essays on the Encounter between Christianity and Science (Berkeley: Univ. of California 
Press, 1986), 154 f. 

William B. Ashworth, Jesuit Science in the Age of Galileo (Kansas City: Lowell 
Press, 1986), 5. 



Jesuits on the Moon <& 31 



cal science finds its origins with the observatory established at the 
Roman College at the time of Clavius. The current Vatican Observa- 
tory was refounded by Pope Leo XIII in 1891 and moved to Castel 
Gandolfo in the 1930s. There are also Vatican Observatory sites at 
the University of Arizona at Tucson, Arizona, and on Mona Kea on 
the island of Hawaii. Many of the current scientists associated with 
the Vatican Observatory are Jesuits, as is the director, George Coyne, 
of the Maryland Province. 

Perhaps one of the best-known Jesuit scientists of the twenti- 
eth century was Pierre Teilhard de Chardin (1881-1955), whose 
writings attempted to bridge the gap between the world of science 
and the world of theology. Interestingly enough, some recent com- 
mentators have seen in some of Teilhard's remarks about scientists 
being linked together in a 'Vast organic system" as a hint of our 
contemporary global interconnectedness via the Internet. 

Jesuit scientists in Europe have had a tradition of regular 
meetings and host their own Website (www.jesuitsinscience.org), 
and a number of U.S. Jesuit mathematicians and lay colleagues have 
met as the Clavius Group since around 1970. 65 

Although not exactly "scientific" ministries in the commonly 
understood sense, I think it is also important to acknowledge the 
Society's work in two areas that make use of modern technology. 
The Vatican Radio, founded in 1931, was entrusted as a specific 
ministry to the Society. There are also the various spiritual ministries 
conducted by Jesuits via the Internet. Perhaps the most widely 
accessed Website of these electronic ministries is Sacred Space 
(www.sacredspace.ie), sponsored by the Irish Jesuits. 66 

Educational Challenges: Jesuit Formation 
and Academic Institutions 

Early Jesuit education was innovative in introducing into 
universities the study of mathematics alongside philosophy and 



See the Website at: www.faculty.fairfield.edu/jmac/cl/clavius.htm. 

Two other sites (among numerous others) focusing on Jesuit spirituality are 
at Creighton University (www.creighton.edu/CollaborativeMinistry/online.html) and 
at the Singapore Jesuit Website (www.jesuit.org.sg). 



32 ^ Dennis C. Smolarski, S.J. 



physics. 67 Especially in the first 1586 Ratio, mathematics was pre- 
sented as a key to understanding physical reality as well as the 
model of correct rational procedure, 68 in this way serving the under- 
standing of the physical world as well as of ultimate, that is, meta- 
physical, reality. But, as already noted, merely prescribing that 
mathematics be taught in a Jesuit university did not eliminate all the 
anti-mathematical prejudices of scholars from other disciplines. 

The tradition of mathematics and the science that is part of the 

Society's heritage raises for me some questions about the present, 

both for the formation of Jesuits and for the formation of students in 

our schools. One foundational 

*— ™— — — — question is whether the current 

Centuries ago, the Church guidelines (that is, core-curriculum 

seemed to be an enemy of , requirements) in mathematics, sci- 

science and technology, with ence, and technology are appro- 

the condemnation of Galileo's priate for the contemporary 

thesis in the seventeenth world? It seems that Clavius 

century and Gregory XVI's would have preferred a more rig- 

more recent prohibition of orous curriculum than what the 

railroads and gas lights in 1599 Ratl0 > in fact ' Prescribed. Per- 

the Papal States in the early- ha P s the final u version wa * more 
. . .1 . realistic, given the variety of coun- 

nineteenth century. . , . , T i 

tries in which Jesuits were estab- 

^ — — — ^— ^— lishing schools, but, as noted ear- 
lier, some have seen the final re- 
quirements as giving in to pressures of the culture of the sixteenth 
century. 

In our contemporary world that is so dependent on technol- 
ogy, what should be the minimum background in mathematics, 
science, and technology for Jesuits in formation? 69 What should be 



67 

Dear, Discipline and Experience, 35. 
68 Feldhay, Galileo and the Church, 222. 



69 

All Jesuit scholastics in formation currently take a significant number of 
philosophy courses to provide a foundation for studying theology. Such courses are 
required even though few Jesuits ever teach philosophy and some find philosophy 
quite difficult. Is it not also reasonable to recommend, and even require at least on an 
assistancy level, some minimum number of mathematics, science, and technology 
courses to equip Jesuits to understand our technologically dependent world, 
especially since Jesuits will be in leadership roles (as priests and teachers) in that 



Jesuits on the Moon <& 33 



the minimum required for students in Jesuit secondary schools and 
universities? Are there other modern technical disciplines that may 
play the same role for the twenty-first century as mathematics did 
for the seventeenth and how should courses in these disciplines be 
introduced into the formation of Jesuits and into the curriculum of 
Jesuits schools? 70 

Needless to say, requiring more mathematics and technical 
courses means having instructors who can make the technical sub- 
jects come alive for students, and 
such instructors are not always *"** 

easy to find and retain. (This is a And in a world in which 

problem Clavius addressed over science and technology are 

four centuries ago in regard to commonplace, leadership in 

mathematics in De re mathematica tomorrow's world demands 

instructio.) In addition, recently familiarity with mathematics 
published reports about the com- and technology and with the 
petency of U.S. primary students wa ys it helps or harms 

in mathematics when compared human progress. 

with students in other countries 

imply that many secondary -— ■— — — — 
schools or colleges may need to 

provide students with significant assistance for them to achieve a 
desired minimal mathematical and scientific competency. 

One of Ignatius's principles for choosing ministries was "the 
greater good — the magis" (ConsCN C 622f., passim). In a world where 
more and more people are leaving organized religion behind, per- 
haps one of the greatest goods that Jesuits and students of Jesuit 
schools could choose to pursue is making use of the language of 
mathematics, science, and technology to begin a conversation with 



world? Some Jesuits may find it difficult (but, I hope, not impossible) to complete, for 
example, two courses in calculus, a lab-science course, and a course in computer 
programming, but the resulting experience of the world of mathematics, science, and 
technology, albeit cursory, may well be worth any difficulty. In this way, they may be 
at least minimally equipped (beyond being able to use a word processor, send e-mail, 
or surf the Net) to interact with a world ever more based on the mathematical 
sciences and dependent on technology. 

I attempted to address the issues of contemporary technical disciplines in 
Jesuit schools in "The Ratio Studiorum and New Technology: Opportunities and 
Challenges," Explore (Journal of the Santa Clara University Bannan Center) 4, no. 1 
(Fall 2000): 22-30. (Available via: www.scu.edu/bannancenter/publications/explore) 



34 <0> Dennis C. Smolarski, SJ. 



people of little or no faith and together tackle the problems of our 
global society, especially issues of justice. As one example, in a world 
in which some companies make significant profits selling virus- 
protection software because bright individuals take delight in wreak- 
ing havoc in our electronically interdependent world, how can 
Jesuits and Jesuit alumni influence the conversation about new 
sources of electronic evil and electronic terrorism in our world? 

In some of my daydreams, I am, perhaps, as unrealistically 
optimistic about mathematics (and science) as Clavius seems to have 
been, but I have also wondered what impact and symbolic statement 
would be made if, in Jesuit schools, there were more Jesuits teaching 
mathematics, science, and technology than Jesuits teaching theology. 
I continue to find people who seem to be amazed and confused 
when, after they ask me, "What do you teach?" I respond, "Mathe- 
matics and computer science." Their retort is usually, "But I thought 
you are a priest, so why are you teaching math?" Such a response 
seems to reflect a contemporary perception about Jesuits and science 

that appears to be in stark contrast 
^_______^^^ to the Society's reputation in the 

_, . , /« , . , „ seventeenth century as a society of 

That is what helping souls sdence what kind of paradigm 

is about, and that is where shift wouM occur today if students 

we may seek and, yes, even saw non .j eS uits as dedicated 

be able to "find God." enough to their faith to obtain the 

^ required competency to teach reli- 

gious subjects and saw Jesuits as 
dedicated enough to the often perceived a-religious world of mathe- 
matics, science, and technology to dedicate their lives to these 
subjects as well. Recent advances and developments in the world of 
mathematics and science may mean that the Society may never be 
able to regain its reputation about being a major scientific society, 
although there may continue to be individual Jesuits who will be 
known as excellent scientists. Yet I hope that, institutionally, the 
Society will continue to commit its energies and willing Jesuits to 
engage with the world of mathematics, science, and technology as 
one area where the "greater good" can be achieved in a world ever 
more dependent on these scholarly disciplines. 



Jesuits on the Moon ^ 35 



VI. Concluding Thoughts 

Unlike the debates about mathematics in the sixteenth cen- 
tury, today there is little disagreement about the appropri- 
ateness of disciplines such as mathematics or other technical 
or scientific fields being offered in a university or about their aca- 
demic stature. Centuries ago, the Church seemed to be an enemy of 
science and technology, with the condemnation of Galileo's thesis in 
the seventeenth century and Gregory XVI's more recent prohibition 
of railroads and gas lights in the Papal States in the early-nineteenth 
century. 71 But in the twentieth century, the Church has taken a 
significantly different approach. 

Perhaps it was John XXIII who introduced the new emphasis 
when, in his 1963 encyclical Pacem in terris, he wrote: "[T]he progress 
of science and the inventions of technology show above all the 
infinite greatness of God. . . . And since our present age is one of 
outstanding scientific and technical progress and excellence, one will 
not be able to . . . work effectively from within unless he is scientifi- 
cally competent, technically capable and skilled in the practice of his 
own profession" (no. 3, 148). The 1990 apostolic constitution Ex corde 
Ecclesiee speaks to the work of Catholic universities in the fields of 
science and technology (see nos. 7, 18, 45). The existence of a Vatican 
Website is a welcome sign that the Church has embraced technology 
to help spread the Gospel message. The Ignatian tradition of "find- 
ing God in all things," even in mathematics and related scientific and 
technical disciplines, is accepted without debate today. Thus, per- 
haps the more important questions deal with the opportunities and 
challenges that studying such disciplines presents to Jesuit schools 
and their students. 

The renowned anthropologist Margaret Mead once said, "The 
solution of adult problems tomorrow depends upon the way we 
raise our children today." We cannot deny that the future leaders of 
corporations and nations are those students in school today. And in 
a world in which science and technology are commonplace, leader- 
ship in tomorrow's world demands familiarity with mathematics and 
technology and with the ways it helps or harms human progress. 



71 

See Hans Kuhner, Encyclopedia of the Papacy (New York: Philosophical 
Library Inc., 1958), 225. 



36 ^ Dennis C. Smolarski, SJ. 



Today's science and technology provide opportunities never 
before possible in our world. The early Jesuits saw education as a 
way to transform society, and the 1599 Ratio provided structures to 
provide an excellent education. In a sense, including mathematics in 
the Ratio forced Jesuits and their students to become familiar with 
this foundational language used by intellectuals of a world on the 
brink of what we now call "the scientific revolution." Through the 
mathematical sciences, Jesuits and their students became engaged, 
perhaps unknowingly, with a culture that was only beginning to 
make its influence felt, the culture of Galileo and Newton, among 
others. 

Near the end of the Constitutions, Ignatius speaks about vari- 
ous means to glorify God and to preserve the Society. While speak- 
ing about such religious topics, Ignatius noted that "the human 
means ought to be sought with diligence, especially well-grounded 
and solid learning" (C 814 v4 ). The Ratio studiorum provided a plan to 
obtain "well-grounded and solid learning," and the influence of 
Clavius enabled students in Jesuits schools to be "well-grounded" in 
the newly developing mathematical sciences. 

The Constitutions also remind us that "the end of learning 
which is acquired in this Society is ... to help the souls of its own 
members and those of their neighbors" (C 351 v2 ). Whatever helps 
build up God's Kingdom on earth, whatever helps ensure that God's 
justice will prevail, whatever helps promote peace and unity among 
peoples and relieves pain, disease, and poverty, whether it involves 
the classics or mathematics or the latest modern technology, that is 
what "helping souls" is about, and that is where we may seek and, 
yes, even be able to "find God." 



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38 



Appendix 2: "De mathematicis" [On Mathematics] 

(from the 1586 first draft of the Ratio studiorum) 

[1] The Constitutions (C 451) reads thus: "Logic, physics, metaphysics, and 
moral philosophy will be treated, and also mathematical topics, insofar as they 
are in accord with the end proposed to us/' 

Nevertheless, they seem to be in accord not just a little, not only because 
without mathematics our academies would be lacking a great ornament, and 
indeed they would even be mutilated, since there is almost no moderately 
celebrated academy, in which the mathematical disciplines do not have their 
own (and indeed the highest) place; but even much more, because the other 
sciences also very much need the help of mathematics. For indeed, the mathe- 
matical disciplines supply and explain to the poets the rising and setting of 
heavenly bodies; to historians the shape and distance of places; to those who 
analyze (analyticis) examples of solid proofs (demonstrationes); to political leaders 
easily admired techniques to manage both domestic and military affairs well; to 
physicists the forms and distinctions of heavenly revolutions, of light, of colors, 
of transparent media, of sounds; to metaphysicians the number of spheres and 
intelligences; to theologians the major parts of the divine handiwork; to law 
and ecclesiastical custom the accurate reckoning of time. For the meantime, we 
pass over the benefits which flow to the republic from the labor of mathemati- 
cians in the healing of diseases, in voyages by sea, in the pursuit of farmers. 
Therefore, an effort must be made so that, just like the other disciplines (facilita- 
tes), mathematics also may flourish in our schools (gymnasiis), so that from this 
also Ours will become more suited for serving the various interests of the 
Church; especially since it is not a little unseemly that we lack professors who 
are capable of presenting a lecture about mathematical topics, longed for in so 
many, such famous, cities. At Rome also, if you subtract one or perhaps a 
second person, there will be hardly any one of those left who is qualified either 
to instruct about these disciplines, or to be at hand for the Apostolic See, when 
there is a discussion about ecclesiastical times. 

[2] So that we may remedy such scarcity and want, we require two mathe- 
matics professors in the Roman College. Let one of these prepare a short course 
(curriculum) of mathematical topics for a year and a half with daily lectures to 
be heard by Ours and by externs; the professor should begin this course after 
the Pasch of the Resurrection in the morning at first school hour for students of 
logic; because at this time generally they are preparing themselves for the 
Posterior analytics, which without mathematical examples can scarcely be 
understood; and since they may be at that time a bit more advanced, they seem 
not unequal to the burden of three lectures. Nevertheless, it is appropriate that 
things be arranged that some of the thornier Elements of Euclid be always 
seasoned by an interpretation either of geography or of the sphere; since in 
particular these topics do not greatly need knowledge of all the principles of 



The translation of this passage is taken from collections of translations that 
appeared in Science in Context 15, no. 3 (2002): 459-64. 

39 



40 ^ Dennis C. Smolarski, SJ. 



Euclid, but of certain of the first [principles], which after around two months 
will have been explained. After this, of the three-quarters of an hour to which a 
mathematical lecture is limited, to the two earlier [topics], the sphere or other 
more acceptable topics of that sort should be handed over, and this arrange- 
ment should be persevered even to the end of the studies. Afterwards, during 
the second year, the remaining part of the compendium of mathematics, to be 
completed by Fr. Clavius, will be expounded to the same students, who then 
will be studying physics, in the first hour of the classes after the midday meal. 
When, however, Easter approaches, let there be added for the benefit of new 
students of logic a second early morning lecture, in which the compendium of 
mathematics is begun again. This presentation and repetition in the same order 
is to be observed each year. 

[3] Let a second professor, who could only be Fr. Clavius, be appointed; let 
him provide fuller teaching about mathematical topics over three years, and 
teach privately about eight or ten of Ours, who are at least of average ability 
and not averse to mathematics, and have studied philosophy; these should be 
recruited from various provinces, one from each one, if it is possible. And there 
will be not a few who will be eager to be of the number of these [special 
students], if, after philosophy in the time others are teaching humane letters, 
they devote themselves to mathematics, then also to theology; in this way, 
surely, as in the first two years, let them study nothing other than mathematics. 
But in the third year, [they will attend] also two lectures of scholastic theology 
with a brief repetition of them, which will take place only in the schools; but 
the entire remainder of the day they give themselves to mathematics. After- 
wards, the excellent mathematicians of this academy will go forth, who will 
disseminate this discipline into all provinces to which they will return, and they 
will uphold the reputation of Ours, if at any time it behooves them to speak 
about mathematics. And it will not be a problem for any province to devote 
some one of their philosophers also for a third year to mathematics, with the 
hope of such excellent fruit. 



Appendixes -& 41 

Appendix 3: Excerpts from "Rules for Mathematics" 

from the definitive Ratio Studiorum of 1599 

Rules for the Professor of Mathematics 

1. What Authors Are to Be Explained, and at What Time and to What Stu- 
dents. Let him explain in class to the students of physics for about three- 
quarters of an hour the Elements of Euclid. In these [explanations], after they 
have become somewhat familiar during two months, let him add something of 
geography or of the sphere or other matters which are wont to be heard gladly, 
and this along with Euclid either on the same day or on alternate days. 

2. Problems. And let him arrange that every month or every other month 
some one of the students before a large gathering of students of philosophy and 
theology has some famous mathematical problem to work out and afterwards, if 
it seems well, to defend his solution. 

3. Repetition. Once a month and generally on Saturday in place of the lecture, 
let the principal points that have been explained during that month be publicly 
repeated. 



Rules for the Provincial Superior 

20. Students and the Time for Mathematics. In the second year of philosophy 
all the students of philosophy shall attend class in mathematics for three- 
quarters of an hour. If there are some, moreover, who are fit and inclined 
towards these studies, let them be practiced in them in private lessons after the 
end of the course. 



42 ^ Dennis C. Smolarski, SJ. 

•Primary Sources and Translations 

Documents of Clavius 

Latin: "Modus quo disiplineae mathematics in scholis Societatis possent promo- 
ueri." Doc. 34 in Monumenta paedagogica Societatis Iesu quae primam rationem 
studiorum anno 1586 editam praecessere. Edited by C. Gomez-Rodeles et al., 471-74. 
Madrid: Typis Augustini Avrial, 1901. 

"De re mathematica instructio." Doc. 35 in Monumenta paedagogica 
Societatis Iesu quae primam rationem studiorum anno 1586 editam praecessere. Edited 
by C. Gomez-Rodejes et al, 474-76. Madrid: Typis Augustini Avrial, 1901. 

These sources also appear in Monumenta paedagogica Societatis Iesu. Edited 
by Ladislaus Lukacs, S.J., 7:109-22. Rome: Institutum Historicum Societatis Iesu, 
1992. 

English: "A Method of Promoting Mathematical Studies in the Schools of the 
Society." Doc. 34 in Bulletin of the American Association of Jesuit Scientists (Eastern 
Section) 18, no. 4 (May 1941): [203]-[206] 

"On Teaching Mathematics." Translation made by Edwin Cuffe, S.J., 
with the advice of Edward H. Nash, S.J., and presented by Edward C. Phillips, 
S.J. Doc. 35 in Bulletin of the American Association of Jesuit Scientists (Eastern 
Section) 18, no. 4 (May 1941): [206]-[208]. 

These documents, translated by Dennis C. Smolarski, S.J., are also found 
in Science in Context 15, no. 3 (2002): 465-70. 

Another translation of the first two-thirds of Doc. 34 is found in "Mathe- 
matics and Platonism in the Sixteenth-Century Italian Universities and in Jesuit 
Educational Policy," by A. C. Crombie. n PI I M ATA [PrismataJ. Natur- 
wissenschaftsgeschichtliche Studien (Festschrift fur Willy Hartner), 65 f. 

Ratio studiorum 

Latin: Ratio atque institutio studiorum Societatis Iesu (1586, 1586B, 1591, 1599). Vol. 
5 in the Monumenta paedagogica Societatis Iesu. Edited by Ladislaus Lukacs, S.J. 
Rome: Institutum Historicum Societatis Iesu, 1986. 

English: Edward A. Fitzpatrick, ed. St. Ignatius and the "Ratio Studiorum," New 
York: McGraw-Hill Book Co., Inc., 1933. 

This volume includes the translation of the 1599 Ratio made by A. R. Ball. 

English excerpts of the sections on mathematics of the various Ratios, 
translated by Dennis C. Smolarski, S.J., can be found in Science in Context, 15, 
no. 3 (2002): 459-64. 



Past Issues: Studies in the Spirituality of Jesuits 

(For prices, see inside back cover.) 

1/1 Sheets, Profile of the Contemporary Jesuit (Sept. 1969) 
1/2 Ganss, Authentic Spiritual Exercises: History and Terminology (Nov. 1969) 
2/1 Burke, Institution and Person (Feb. 1970) 
2/2 Futrell, Ignatian Discernment (Apr. 1970) 

2/3 Lonergan, Response of the Jesuit as Priest and Apostle (Sept. 1970) 
3/1 Wright, Grace of Our Founder and the Grace of Our Vocation (Feb. 1971) 
3/2 O'Flaherty, Some Reflections on Jesuit Commitment (Apr. 1971) 
3/4 Toner, A Method for Communal Discernment of God's Will (Sept. 1971) 
3/5 Sheets, Toward a Theology of the Religious Life (Nov. 1971) 
4/2 Two Discussions: I. Spiritual Direction, II. Leadership and Authority (Mar. 1972) 
4/3 Orsy, Some Questions about the Purpose and Scope of the General Congregation (June 1972) 
4/4 Ganss, Wright, O'Malley, O'Donovan, Dulles, On Continuity and Change: A Symposium 
(Oct. 1972) 
5/1-2 O'Flaherty, Renewal: Call and Response (Jan.-Mar. 1973) 
5/3 Arrupe, McNaspy, The Place of Art in Jesuit Life (Apr. 1973) 
5/4 Haughey, The Pentecostal Thing and Jesuits (June 1973) 

5/5 Orsy, Toward a Theological Evaluation of Communal Discernment (Oct. 1973) 
6/3 Knight, Joy and Judgment in Religious Obedience (Apr. 1974) 
7/1 Wright, Ganss, Orsy, On Thinking with the Church Today (Jan. 1975) 
7/2 Ganss, Christian Life Communities from the Sodalities (Mar. 1975) 
7/3 Connolly, Contemporary Spiritual Direction: Scope and Principles (June 1975) 
7/5 Buckley, The Confirmation of a Promise; Padberg, Continuity and Change in General 

Congregation XXXII (Nov. 1975) 
8/1 O'Neill, Acatamiento: Ignatian Reverence (Jan. 1976) 
8/2-3 De la Costa, Sheridan, and others, On Becoming Poor: A Symposium on Evangelical Poverty 
(Mar.-May 1976) 
8/4 Faricy, Jesuit Community: Community of Prayer (Oct. 1976) 
9/1-2 Becker, Changes in U.S. Jesuit Membership, 1958-75; Others, Reactions and Explanations 
(Jan.-Mar. 1977) 
9/4 Connolly, Land, Jesuit Spiritualities and the Struggle for Social Justice (Sept. 1977). 
9/5 Gill, A Jesuit's Account of Conscience (Nov. 1977) 

10/1 Kammer, "Burn-Out"— Dilemma for the Jesuit Social Activist (Jan. 1978) 
10/4 Harvanek, Status of Obedience in the Society of Jesus; Others, Reactions to Connolly- Land 

(Sept. 1978) 
11/1 Clancy, Feeling Bad about Feeling Good (Jan. 1979) 

11/2 Maruca, Our Personal Witness as Power to Evangelize Culture (Mar. 1979) 
11/3 Klein, American Jesuits and the Liturgy (May 1979) 
11/5 Conwell, The Kamikaze Factor: Choosing Jesuit Ministries (Nov. 1979) 
12/2 Henriot, Appleyard, Klein, Living Together in Mission: A Symposium on Small Apostolic 

Communities (Mar. 1980) 
12/3 Conwell, Living and Dying in the Society of Jesus (May 1980) 
12/4-5 Schineller, Newer Approaches to Christology and Their Use in the Spiritual Exercises (Sept. -No v. 
1980) 



13/1 Peter, Alcoholism in Jesuit Life (Jan. 1981) 

13/3 Ganss, Towards Understanding the Jesuit Brothers' Vocation (May 1981) 

13/4 Reites, St. Ignatius of Loyola and the Jews (Sept. 1981) 

14/1 O'Malley, The Jesuits, St. Ignatius, and the Counter Reformation (Jan. 1982) 

14/2 Dulles, St. Ignatius and Jesuit Theological Tradition (Mar. 1982) 

14/4 Gray, An Experience in Ignatian Government (Sept. 1982) 

14/5 Ivern, The Future of Faith and Justice: Review of Decree Four (Nov. 1982) 

15/1 O'Malley, The Fourth Vow in Its Ignatian Context (Jan. 1983) 

15/2 Sullivan and Faricy, On Making the Spiritual Exercises for Renewal of Jesuit Charisms (Mar. 

1983) 

15/3-4 Padberg, The Society True to Itself: A Brief History of the 32nd General Congregation of the 

Society of Jesus (May-Sept. 1983) 

15/5-16/1 Tetlow, Jesuits' Mission in Higher Education (Nov. 1983-Jan. 1984) 

16/2 O'Malley, To Travel to Any Part of the World: Jeronimo Nodal and the Jesuit Vocation (Mar. 

1984) 

16/3 O'Hanlon, Integration of Christian Practices: A Western Christian Looks East (May 1984) 

16/4 Carlson, "A Faith Lived Out of Doors": Ongoing Formation (Sept. 1984) 

17/1 Spohn, St. Paul on Apostolic Celibacy and the Body of Christ (Jan. 1985) 

17/2 Daley, "In Ten Thousand Places": Christian Universality and the Jesuit Mission (Mar. 1985) 

17/3 Tetlow, Dialogue on the Sexual Maturing of Celibates (May 1985) 

17/4 Spohn, Coleman, Clarke, Henriot, Jesuits and Peacemaking (Sept. 1985) 

17/5 Kinerk, When Jesuits Pray: A Perspective on the Prayer of Apostolic Persons (Nov. 1985) 

18/1 Gelpi, The Converting Jesuit (Jan. 1986). 

18/2 Beirne, Compass and Catalyst: The Ministry of Administration. (Mar. 1986) 

18/3 McCormick, Bishops as Teachers and Jesuits as Listeners (May 1986) 

18/5 Tetlow, The Transformation of Jesuit Poverty (Nov. 1986). 

19/1 Staudenmaier, United States Technology and Adult Commitment (Jan. 1987) 

19/2 Appleyard, Languages We Use: Talking about Religious Experience (Mar. 1987) 

19/5 Endean, Who Do You Say Ignatius Is? Jesuit Fundamentalism and Beyond (Nov. 1987) 

20/1 Brackley, Downward Mobility: Social Implications of St. Ignatius's Two Standards (Jan. 1988) 

20/2 Padberg, How We Live Where We Live (Mar. 1988) 

20/3 Hayes, Padberg, Staudenmaier, Symbols, Devotions, and Jesuits (May 1988) 

20/4 McGovern, Jesuit Education and Jesuit Spirituality (Sept. 1988) 

20/5 Barry, Jesuit Formation Today: An Invitation to Dialogue and Involvement (Nov. 1988) 

21/1 Wilson, Where Do We Belong? United States Jesuits and Their Memberships (Jan. 1989) 

21/2 Demoustier, Calvez, et al., The Disturbing Subject: The Option for the Poor (Mar. 1989) 

21/3 Soukup, Jesuit Response to the Communication Revolution (May 1989) 

22/1 Carroll, The Spiritual Exercises in Everyday Life Qan. 1990) 

22/2 Bracken, Jesuit Spirituality from a Process Prospective (March 1990) 

22/3 Shepherd, Fire for a Weekend: An Experience of the Exercises (May 1990) 

22/4 O'Sullivan, Trust Your Feelings, but Use Your Head (Sept. 1990) 

22/5 Coleman, A Company of Critics: Jesuits and the Intellectual Life (Nov. 1990) 

23/1 Houdek, The Road Too Often Traveled (Jan. 1991) 

23/2 DiGiacomo, Ministering to the Young (March 1991) 

23/3 Begheyn and Bogart, A Bibliography on St. Ignatius's Spiritual Exercises (May 1991) 

23/4 Shelton, Reflections on the Mental Health of Jesuits (Sept. 1991) 

23/5 Toolan, "Nature Is a Heraclitean Fire" (Nov. 1991) 



24/1 Houdek, Jesuit Prayer and Jesuit Ministry: Context and Possibilities Qan. 1992) 

24/2 Smolich, Testing the Water: Jesuits Accompanying the Poor (March 1992) 

24/3 Hassel, Jesus Christ Changing Yesterday, Today, and Forever (May 1992) 

24/4 Shelton, Toward Healthy Jesuit Community Living (Sept. 1992) 

24/5 Cook, Jesus' Parables and the Faith That Does Justice (Nov. 1992) 

25/2 Donahue, What Does the Lord Require? (March 1993)— ONCE AGAIN AVAILABLE 

25/3 Padberg, Ignatius, the Popes, and Realistic Reverence (May 1993) 

25/4 Stahel, Toward General Congregation 34 (Sept. 1993) 

25/5 Baldovin, Christian Liturgy: An Annotated Bibliography (Nov. 1993) 

26/1 Tetlow, The Most Postmodern Prayer Qan. 1994) 

26/2 Murphy, The Many Ways of Justice (March 1994) 

26/3 Staudenmaier, To Fall in Love with the World (May 1994) 

26/4 Foley, Stepping into the River (Sept. 1994) 

26/5 Landy, Myths That Shape Us (Nov. 1994) 

27/1 Daley, "To Be More like Christ" (Jan. 1995) 

27/2 Schmidt, Portraits and Landscapes (March 1995) 

27/3 Stockhausen, I'd Love to, but I Don't Have the Time (May 1995) 

27/4 Anderson, Jesuits in Jail, Ignatius to the Present (Sept. 1995) 

27/5 Shelton, Friendship in Jesuit Life (Nov. 1995) 

28/1 Begheyn, Bibliography on the History of the Jesuits Qan. 1996) 

28/3 Clooney, In Ten Thousand Places, in Every Blade of Grass (May 1996) 

28/4 Starkloff, "As Different As Night and Day" (Sept. 1996) 

28/5 Beckett, Listening to Our History (Nov. 1996) 

29/1 Hamm, Preaching Biblical Justice Qan. 1997) 

29/2 Padberg, The Three Forgotten Founders (March 1997) 

29/3 Byrne, Jesuits and Parish Ministry (May 1997) 

29/4 Keenan, Are Informationes Ethical? (Sept. 1997) 

29/5 Ferlita, The Road to Bethlehem-Is It Level or Winding? (Nov. 1997) 

30/1 Shore, The Vita Christi of Ludolph of Saxony and Its Influence on the Spiritual Exercises of 

Ignatius of Loyola Qan. 1998) 

30/2 Starkloff, "I'm No Theologian, but . . . (or So . . . )?" (March 1998) 

30/3 Torrens, The Word That Clamors (May 1998) 

30/4 Petrik, "Being Sent" (Sept. 1998) 

30/5 Jackson, "One and the Same Vocation" (Nov. 1998) 

31/1 Clifford, Scripture and the Exercises Qan. 1999) 

31/2 Toohig, Physics Research, a Search for God (March 1999) 

31/3 Fagin, Fidelity in the Church— Then and Now (May 1999) 

31/4 Schineller, Pilgrim Journey of Ignatius (Sept. 1999) 

31/5 Fullam, Juana, S.J.: Status of Women in the Society (Nov. 1999) 

32/1 Langan, The Good of Obedience in a Culture of Autonomy Qan. 2000) 

32/2 Blake, Listen with Your Eyes (March 2000) 

32/3 Shelton, When a Jesuit Counsels Others (May 2000) 

32/4 Barry, Past, Present, and Future (Sept. 2000) 

32/5 Starkloff, Pilgrimage Re-envisioned (Nov. 2000) 

33/1 Kolvenbach et al., Faith, Justice, and American Jesuit Higher Education Qan. 2001) 

33/2 Keenan, Unexpected Consequences: Persons's Christian Directory (March 2001) 

33/3 Arrupe, Trinitarian Inspiration of the Ignatian Charism (May 2001) 



33/4 Veale, Saint Ignatius Asks, "Are You Sure You Know Who I Am?" (Sept. 2001) 

33/5 Barry and Keenan, How Multicultural Are We? (Nov. 2001) 

34/1 Blake, "City of the Living God" (Jan. 2002) 

34/2 Clooney, A Charism for Dialog (March 2002) 

34/3 Rehg, Christian Mindfulness (May 2002) 

34/4 Brackley, Expanding the Shrunken Soul (Sept. 2002) 

34/5 Bireley, The Jesuits and Politics in Time of War (Nov. 2002) 

35/1 Barry, Jesuit Spirituality for the Whole of Life (Jan. 2003) 

35/2 Madden/Janssens, The Training of Ours in the Sacred Liturgy (March 2003) 

35/3 Marcouiller, Archbishop with an Attitude (May 2003) 

35/4 Modras, A Jesuit in the Crucible (Sept. 2003) 

35/5 Lucas, Virtual Vessels, Mystical Signs (Nov. 2003) 

36/1 Rausch, Christian Life Communities for Jesuit University Students? (Spring 2004) 

36/2 Bernauer, The Holocaust and the Search for Forgiveness (Summer 2004) 

36/3 Nantais, "Whatever!" Is Not Ignatian Indifference (Fall 2004) 

36/4 Lukacs, The Incarnational Dynamic of the Constitutions (Winter 2004) 

37/1 Smolarski, Jesuits on the Moon (Spring 2005) 



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